ESAIM: Probability and Statistics (ESAIM: P&S)

Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps

Subramaniam Saravanakumar and Pagavathigounder Balasubramaniam
International Journal of Nonlinear Sciences and Numerical Simulation 21 (7-8) 727 (2020)
DOI: 10.1515/ijnsns-2019-0141
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Neutral stochastic partial differential equations with delay driven by Rosenblatt process in a Hilbert space

Guangjun Shen and Yong Ren
Journal of the Korean Statistical Society 44 (1) 123 (2015)
DOI: 10.1016/j.jkss.2014.06.002
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A Weak Convergence to Hermite Process by Martingale Differences

Xichao Sun and Ronglong Cheng
Advances in Mathematical Physics 2014 1 (2014)
DOI: 10.1155/2014/307819
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Handbook of High-Frequency Trading and Modeling in Finance

Alexis Fauth and Ciprian A. Tudor
Handbook of High-Frequency Trading and Modeling in Finance 221 (2016)
DOI: 10.1002/9781118593486.ch8
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On the rate of convergence to Rosenblatt-type distribution

Vo Anh, Nikolai Leonenko and Andriy Olenko
Journal of Mathematical Analysis and Applications 425 (1) 111 (2015)
DOI: 10.1016/j.jmaa.2014.12.016
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An Optimal Approximation of Rosenblatt Sheet by Multiple Wiener Integrals

Guangjun Shen and Qian Yu
Mediterranean Journal of Mathematics 14 (2) (2017)
DOI: 10.1007/s00009-017-0856-3
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Maximum-likelihood estimators and random walks in long memory models

Karine Bertin, Soledad Torres and Ciprian A. Tudor
Statistics 45 (4) 361 (2011)
DOI: 10.1080/02331881003768750
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Generalized continuous time random walks and Hermite processes

Zhenlong Chen, Lin Xu and Dongjin Zhu
Statistics & Probability Letters 99 44 (2015)
DOI: 10.1016/j.spl.2014.12.027
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A strong convergence to the Rosenblatt process

Johanna Garzón, Soledad Torres and Ciprian A. Tudor
Journal of Mathematical Analysis and Applications 391 (2) 630 (2012)
DOI: 10.1016/j.jmaa.2012.02.040
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Option pricing under a Gamma-modulated diffusion process

Pilar Iglesias, Jaime San Martín, Soledad Torres and Frederi Viens
Annals of Finance 7 (2) 199 (2011)
DOI: 10.1007/s10436-011-0176-8
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Non-central limit theorem of the weighted power variations of Gaussian processes

Iltae Kim, Hyun Suk Park and Yoon Tae Kim
Journal of the Korean Statistical Society 43 (2) 215 (2014)
DOI: 10.1016/j.jkss.2013.09.001
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Approximation of the Rosenblatt process by semimartingales

Litan Yan, Yumiao Li and Di Wu
Communications in Statistics - Theory and Methods 46 (9) 4556 (2017)
DOI: 10.1080/03610926.2015.1088032
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Approximation of the Rosenblatt Sheet

Guangjun Shen, Xiuwei Yin and Litan Yan
Mediterranean Journal of Mathematics 13 (4) 2215 (2016)
DOI: 10.1007/s00009-015-0576-5
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Donsker Type Theorem for the Rosenblatt Process and a Binary Market Model

Soledad Torres and Ciprian A. Tudor
Stochastic Analysis and Applications 27 (3) 555 (2009)
DOI: 10.1080/07362990902844371
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Noncentral limit theorem for the cubic variation of a class of self-similar stochastic processes

Khalifa Es-Sebaiy, Khalifa Es-Sebaiy, C A Tudor and C A Tudor
Теория вероятностей и ее применения 55 (3) 507 (2010)
DOI: 10.4213/tvp4239
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Noncentral Limit Theorem for the Cubic Variation of a Class of Self-Similar Stochastic Processes

K. Es-Sebaiy and C. A. Tudor
Theory of Probability & Its Applications 55 (3) 411 (2011)
DOI: 10.1137/S0040585X97984978
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Weak convergence to a class of multiple stochastic integrals

Xichao Sun and Litan Yan
Communications in Statistics - Theory and Methods 46 (17) 8355 (2017)
DOI: 10.1080/03610926.2016.1179758
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A White Noise Approach to Stochastic Integration with Respect to the Rosenblatt Process

Benjamin Arras
Potential Analysis 43 (4) 547 (2015)
DOI: 10.1007/s11118-015-9484-3
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An approximation to the Rosenblatt process using martingale differences

Chao Chen, Liya Sun and Litan Yan
Statistics & Probability Letters 82 (4) 748 (2012)
DOI: 10.1016/j.spl.2011.12.006
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Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process

Zhi Li, Litan Yan and Xianghui Zhou
Frontiers of Mathematics in China 13 (1) 87 (2018)
DOI: 10.1007/s11464-017-0672-x
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Lévy Matters V

Makoto Maejima
Lecture Notes in Mathematics, Lévy Matters V 2149 1 (2015)
DOI: 10.1007/978-3-319-23138-9_1
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Variations and estimators for self-similarity parameters via Malliavin calculus

Ciprian A. Tudor and Frederi G. Viens
The Annals of Probability 37 (6) (2009)
DOI: 10.1214/09-AOP459
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Random homogenization and convergence to integrals with respect to the Rosenblatt process

Yu Gu and Guillaume Bal
Journal of Differential Equations 253 (4) 1069 (2012)
DOI: 10.1016/j.jde.2012.05.007
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On the distribution of the Rosenblatt process

Makoto Maejima and Ciprian A. Tudor
Statistics & Probability Letters 83 (6) 1490 (2013)
DOI: 10.1016/j.spl.2013.02.019
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Regularization and integral representations of Hermite processes

Vladas Pipiras and Murad S. Taqqu
Statistics & Probability Letters 80 (23-24) 2014 (2010)
DOI: 10.1016/j.spl.2010.09.008
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Parameter estimation for the Rosenblatt Ornstein–Uhlenbeck process with periodic mean

Radomyra Shevchenko and Ciprian A. Tudor
Statistical Inference for Stochastic Processes 23 (1) 227 (2020)
DOI: 10.1007/s11203-019-09200-5
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Retarded stochastic differential equations with infinite delay driven by Rosenblatt process

R. Sakthivel, P. Revathi, Yong Ren and Guangjun Shen
Stochastic Analysis and Applications 36 (2) 304 (2018)
DOI: 10.1080/07362994.2017.1399801
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A Note on Distributions in the Second Chaos

Pauliina Ilmonen and Lauri Viitasaari
Symmetry 11 (12) 1487 (2019)
DOI: 10.3390/sym11121487
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Wiener integrals with respect to the Hermite random field and applications to the wave equation

Jorge Clarke De la Cerda and Ciprian A. Tudor
Collectanea Mathematica 65 (3) 341 (2014)
DOI: 10.1007/s13348-014-0108-9
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Dissipative Stochastic Evolution Equations Driven by General Gaussian and Non-Gaussian Noise

S. Bonaccorsi and C. A. Tudor
Journal of Dynamics and Differential Equations 23 (4) 791 (2011)
DOI: 10.1007/s10884-011-9217-2
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Weak convergence to Rosenblatt sheet

Guangjun Shen, Xiuwei Yin and Dongjin Zhu
Frontiers of Mathematics in China 10 (4) 985 (2015)
DOI: 10.1007/s11464-015-0458-y
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A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter

J.-M. Bardet and C.A. Tudor
Stochastic Processes and their Applications 120 (12) 2331 (2010)
DOI: 10.1016/j.spa.2010.08.003
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Bayesian estimation of self-similarity exponent

Natallia Makarava, Sabah Benmehdi and Matthias Holschneider
Physical Review E 84 (2) (2011)
DOI: 10.1103/PhysRevE.84.021109
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Limiting measure and stationarity of solutions to stochastic evolution equations with Volterra noise

P. Čoupek
Stochastic Analysis and Applications 36 (3) 393 (2018)
DOI: 10.1080/07362994.2017.1409124
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Recent Advances in Intuitionistic Fuzzy Logic Systems

E. Lakhel and A. Tlidi
Studies in Fuzziness and Soft Computing, Recent Advances in Intuitionistic Fuzzy Logic Systems 372 301 (2019)
DOI: 10.1007/978-3-030-02155-9_24
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Forward integration, convergence and non-adapted pointwise multipliers

Matthijs Pronk and Mark Veraar
Infinite Dimensional Analysis, Quantum Probability and Related Topics 18 (01) 1550005 (2015)
DOI: 10.1142/S0219025715500058
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Non-central limit theorems for quadratic functionals of Hermite-driven long memory moving average processes

T. T. Diu Tran
Stochastics and Dynamics 18 (04) 1850028 (2018)
DOI: 10.1142/S0219493718500284
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Lp-valued stochastic convolution integral driven by Volterra noise

Petr Čoupek, Bohdan Maslowski and Martin Ondreját
Stochastics and Dynamics 18 (06) 1850048 (2018)
DOI: 10.1142/S021949371850048X
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Generalized Hermite processes, discrete chaos and limit theorems

Shuyang Bai and Murad S. Taqqu
Stochastic Processes and their Applications 124 (4) 1710 (2014)
DOI: 10.1016/j.spa.2013.12.011
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From intersection local time to the Rosenblatt process

Tomasz Bojdecki, Luis G. Gorostiza and Anna Talarczyk
Journal of Theoretical Probability 28 (3) 1227 (2015)
DOI: 10.1007/s10959-013-0535-7
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On a class of self-similar processes with stationary increments in higher order Wiener chaoses

Benjamin Arras
Stochastic Processes and their Applications 124 (7) 2415 (2014)
DOI: 10.1016/j.spa.2014.02.012
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Stochastic evolution equations with Volterra noise

P. Čoupek and B. Maslowski
Stochastic Processes and their Applications 127 (3) 877 (2017)
DOI: 10.1016/j.spa.2016.07.003
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PRICING DERIVATIVES IN HERMITE MARKETS

STOYAN V. STOYANOV, SVETLOZAR T. RACHEV, STEFAN MITTNIK and FRANK J. FABOZZI
International Journal of Theoretical and Applied Finance 22 (06) 1950031 (2019)
DOI: 10.1142/S0219024919500316
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Stochastic Partial Differential Equations and Related Fields

Petr Čoupek, Bohdan Maslowski and Jana Šnupárková
Springer Proceedings in Mathematics & Statistics, Stochastic Partial Differential Equations and Related Fields 229 147 (2018)
DOI: 10.1007/978-3-319-74929-7_7
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Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

Jean-Marc Bardet and Ciprian Tudor
Journal of Multivariate Analysis 131 1 (2014)
DOI: 10.1016/j.jmva.2014.06.012
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On impulsive Hilfer fractional stochastic differential system driven by Rosenblatt process

S. Saravanakumar and P. Balasubramaniam
Stochastic Analysis and Applications 37 (6) 955 (2019)
DOI: 10.1080/07362994.2019.1629301
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Averaging principle for equation driven by a stochastic measure

V. M. Radchenko
Stochastics 91 (6) 905 (2019)
DOI: 10.1080/17442508.2018.1559320
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Quadratic variations for the fractional-colored stochastic heat equation

Soledad Torres, Ciprian Tudor and Frederi Viens
Electronic Journal of Probability 19 (none) (2014)
DOI: 10.1214/EJP.v19-2698
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Representations of hermite processes using local time of intersecting stationary stable regenerative sets

Shuyang Bai
Journal of Applied Probability 57 (4) 1234 (2020)
DOI: 10.1017/jpr.2020.57
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Selected Works of Murray Rosenblatt

Richard A. Davis, Keh-Shin Lii and Dimitris N. Politis
Selected Works of Murray Rosenblatt 29 (2011)
DOI: 10.1007/978-1-4419-8339-8_6
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Controllability and stability of fractional stochastic functional systems driven by Rosenblatt process

Guangjun Shen, R. Sakthivel, Yong Ren and Mengyu Li
Collectanea Mathematica 71 (1) 63 (2020)
DOI: 10.1007/s13348-019-00248-3
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The Laws of Large Numbers Associated with the Linear Self-attracting Diffusion Driven by Fractional Brownian Motion and Applications

Xichao Sun, Litan Yan and Yong Ge
Journal of Theoretical Probability (2021)
DOI: 10.1007/s10959-021-01126-0
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Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses

Rajesh Dhayal and Muslim Malik
Chaos, Solitons & Fractals 151 111292 (2021)
DOI: 10.1016/j.chaos.2021.111292
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Variations and Hurst index estimation for a Rosenblatt process using longer filters

Alexandra Chronopoulou, Frederi G. Viens and Ciprian A. Tudor
Electronic Journal of Statistics 3 (none) (2009)
DOI: 10.1214/09-EJS423
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A stochastic calculus for Rosenblatt processes

Petr Čoupek, Tyrone E. Duncan and Bozenna Pasik-Duncan
Stochastic Processes and their Applications (2020)
DOI: 10.1016/j.spa.2020.01.004
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Controllability for Time-dependent Neutral Stochastic Functional Differential Equations with Rosenblatt Process and Impulses

El Hassan Lakhel and M. A. McKibben
International Journal of Control, Automation and Systems 17 (2) 286 (2019)
DOI: 10.1007/s12555-016-0363-5
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On a generalized stochastic Burgers' equation perturbed by Volterra noise

Vivek Kumar, Manil T. Mohan and Ankik Kumar Giri
Journal of Mathematical Analysis and Applications 506 (1) 125638 (2022)
DOI: 10.1016/j.jmaa.2021.125638
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Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays

Lakhel El Hassan
Proyecciones (Antofagasta) 38 (4) 665 (2019)
DOI: 10.22199/issn.0717-6279-2019-04-0043
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Existence, uniqueness and stability of impulsive stochastic neutral functional differential equations driven by Rosenblatt process with varying-time delays

El Hassan Lakhel and Abdelmonaim Tlidi
Random Operators and Stochastic Equations 27 (4) 213 (2019)
DOI: 10.1515/rose-2019-2019
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Fractional neutral stochastic differential equations with Caputo fractional derivative: Fractional Brownian motion, Poisson jumps, and optimal control

K. Ramkumar, K. Ravikumar and S. Varshini
Stochastic Analysis and Applications 39 (1) 157 (2021)
DOI: 10.1080/07362994.2020.1789476
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Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

T. Sathiyaraj, JinRong Wang and D. O'Regan
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 151 (1) 217 (2021)
DOI: 10.1017/prm.2020.11
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Existence and Hölder continuity conditions for self-intersection local time of Rosenblatt process

Qian Yu, Guangjun Shen and Xiuwei Yin
Stochastic Analysis and Applications 1 (2021)
DOI: 10.1080/07362994.2021.1973497
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AR(1) processes driven by second-chaos white noise: Berry–Esséen bounds for quadratic variation and parameter estimation

Soukaina Douissi, Khalifa Es-Sebaiy, Fatimah Alshahrani and Frederi G. Viens
Stochastic Processes and their Applications (2020)
DOI: 10.1016/j.spa.2020.02.007
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Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions

Yaozhong Hu, Yanghui Liu and David Nualart
The Annals of Applied Probability 26 (2) (2016)
DOI: 10.1214/15-AAP1114
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Functional limit theorems for generalized variations of the fractional Brownian sheet

Mikko S. Pakkanen and Anthony Réveillac
Bernoulli 22 (3) (2016)
DOI: 10.3150/15-BEJ707
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Approximating the Rosenblatt process by multiple Wiener integrals

Litan Yan, Yumiao Li and Di Wu
Electronic Communications in Probability 20 (none) (2015)
DOI: 10.1214/ECP.v20-3517
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Central and non-central limit theorems for weighted power variations of fractional Brownian motion

Ivan Nourdin, David Nualart and Ciprian A. Tudor
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 46 (4) (2010)
DOI: 10.1214/09-AIHP342
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Donsker type theorem for fractional Poisson process

Héctor Araya, Natalia Bahamonde, Soledad Torres and Frederi Viens
Statistics & Probability Letters 150 1 (2019)
DOI: 10.1016/j.spl.2019.01.036
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Hausdorff and packing dimensions of the images of random fields

Narn-Rueih Shieh and Yimin Xiao
Bernoulli 16 (4) (2010)
DOI: 10.3150/09-BEJ244
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Properties and numerical evaluation of the Rosenblatt distribution

Mark S. Veillette and Murad S. Taqqu
Bernoulli 19 (3) (2013)
DOI: 10.3150/12-BEJ421
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Drift estimation with non-gaussian noise using Malliavin Calculus

Christian Krein
Electronic Journal of Statistics 9 (2) (2015)
DOI: 10.1214/15-EJS1101
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Existence and controllability of impulsive fractional stochastic differential equations driven by Rosenblatt process with Poisson jumps

Rajesh Dhayal and Muslim Malik
Journal of Engineering Mathematics 130 (1) (2021)
DOI: 10.1007/s10665-021-10167-7
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Ergodic Linear-Quadratic Control for a Two Dimensional Stochastic System Driven by a Continuous Non-Gaussian Noise

Tyrone E. Duncan and Bozenna Pasik-Duncan
IFAC-PapersOnLine 53 (2) 2177 (2020)
DOI: 10.1016/j.ifacol.2020.12.2548
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Petr Coupek, Tyrone E. Duncan, Bohdan Maslowski and Bozenna Pasik-Duncan
4973 (2018)
DOI: 10.1109/CDC.2018.8619402
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Exponential behavior of neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process

Ravikumar Kasinathan, Ramkumar Kasinathan, Mahamat Hassan Mahamat Hamit and Mamadou Abdoul Diop
Nonautonomous Dynamical Systems 7 (1) 1 (2020)
DOI: 10.1515/msds-2020-0001
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Conformable fractional stochastic differential equations with control function

Hamdy M. Ahmed
Systems & Control Letters 158 105062 (2021)
DOI: 10.1016/j.sysconle.2021.105062
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K. Anukiruthika and P. Muthukumar
1405 93 (2022)
DOI: 10.1007/978-981-16-5952-2_9
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Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay

Youssef Benkabdi and E. Lakhel
Random Operators and Stochastic Equations 29 (4) 237 (2021)
DOI: 10.1515/rose-2021-2063
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Non symmetric Rosenblatt process over a compact

Héctor Araya, Johanna Garzón and Tania Roa
Communications in Statistics - Theory and Methods 50 (23) 5517 (2021)
DOI: 10.1080/03610926.2020.1734830
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Tyrone E. Duncan and Bozenna Pasik-Duncan
343 (2020)
DOI: 10.1109/CDC42340.2020.9304316
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Stochastic integration with respect to fractional processes in Banach spaces

Petr Čoupek, Bohdan Maslowski and Martin Ondreját
Journal of Functional Analysis 282 (8) 109393 (2022)
DOI: 10.1016/j.jfa.2022.109393
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Noninstantaneous Impulsive Conformable Fractional Stochastic Delay Integro-Differential System with Rosenblatt Process and Control Function

Hamdy M. Ahmed
Qualitative Theory of Dynamical Systems 21 (1) (2022)
DOI: 10.1007/s12346-021-00544-z
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Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps

El Hassan Lakhel
Random Operators and Stochastic Equations 24 (2) 113 (2016)
DOI: 10.1515/rose-2016-0008
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Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

Christian Kuehn, Kerstin Lux and Alexandra Neamţu
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 478 (2259) (2022)
DOI: 10.1098/rspa.2021.0740
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Optimal controls for fractional stochastic differential systems driven by Rosenblatt process with impulses

Rajesh Dhayal, José Francisco Gómez‐Aguilar and Guillermo Fernández‐Anaya
Optimal Control Applications and Methods 43 (2) 386 (2022)
DOI: 10.1002/oca.2805
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Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness

P. Balasubramaniam
Chaos, Solitons & Fractals 157 111960 (2022)
DOI: 10.1016/j.chaos.2022.111960
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Hilfer fractional neutral stochastic partial differential equations with delay driven by Rosenblatt process

Hamdy M. Ahmed
Journal of Control and Decision 9 (2) 226 (2022)
DOI: 10.1080/23307706.2021.1953412
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Advances in Noise Modeling for Stochastic Systems in Optimal Control

Tyrone E. Duncan and Bozenna Pasik-Duncan
La Matematica (2022)
DOI: 10.1007/s44007-022-00025-y
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Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump

Yousef Alnafisah and Hamdy M. Ahmed
International Journal of Nonlinear Sciences and Numerical Simulation (2021)
DOI: 10.1515/ijnsns-2020-0292
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