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All issues Volume 28 (2024) ESAIM: PS, 28 (2024) 75-109 References
Open Access
Issue
ESAIM: PS
Volume 28, 2024
Page(s) 75 - 109
DOI https://doi.org/10.1051/ps/2024004
Published online 04 April 2024
  1. T.E. Harris, Coalescing and noncoalescing stochastic flows in R1. Stochastic Process. Appl. 17 (1984) 187–210. [CrossRef] [MathSciNet] [Google Scholar]
  2. H. Kunita, Cambridge Studies in Advanced Mathematics. Vol. 24 of Stochastic Flows and Stochastic Differential Equations. Cambridge University Press, Cambridge (1990) xiv+346. [Google Scholar]
  3. A.A. Dorogovtsev, Proceedings of Institute of Mathematics of NAS of Ukraine. Mathematics and its Applications. Vol. 66 of Measure-valued Processes and Stochastic Flows. Natsional’na Akademiya Nauk Ukraini, Institut Matematiki, Kyiv (2007) 290. [Google Scholar]
  4. P. Bressloff, Stochastic neural field model of stimulus-dependent variability in cortical neurons. PLoS Computat. Biol. 15 (2019) e1006755. [CrossRef] [Google Scholar]
  5. P. Kotelenez, M.J. Leitman and J.A. Mann, Correlated Brownian motions and the depletion effect in colloids. J. Stat. Mech. Theory Exp. 2009 (2009) 01054. [Google Scholar]
  6. M. Coghi and F. Flandoli, Propagation of chaos for interacting particles subject to environmental noise. Ann. Appl. Probab. 26 (2016) 1407–1442. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Guo and D. Luo, Scaling limit of moderately interacting particle systems with singular interaction and environmental noise. arXiv, 2021. [Google Scholar]
  8. I. Gyöngy and N. Krylov, On the splitting-up method and stochastic partial differential equations. Ann. Probab. 31 (2003) 564–591. [MathSciNet] [Google Scholar]
  9. E. Faou, Analysis of splitting methods for reaction-diffusion problems using stochastic calculus. Math. Comput. 78 (2009) 1467–1483. [CrossRef] [Google Scholar]
  10. I. Gyongy and M. Rasonyi, A note on Euler approximations for SDEs with Holder continuous diffusion coefficients. Stochastic Process. Appl. 121 (2011) 2189–2200. [CrossRef] [MathSciNet] [Google Scholar]
  11. N.Y. Goncharuk and P. Kotelenez, Fractional step method for stochastic evolution equations. Stochastic Processes Applic. 73 (1998) 1–45. [CrossRef] [Google Scholar]
  12. A. Bensoussan, R. Glowinski and A. Rasçanu, Approximation of some stochastic differential equations by the splitting up method. Appl. Math. Optim. 25 (1992) 81–106. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Buckwar, A. Samson, M. Tamborrino, et al., A splitting method for SDEs with locally Lipschitz drift: illustration on the FitzHugh—Nagumo model. Appl. Numer. Math. 179 (2022) 191–220. [CrossRef] [MathSciNet] [Google Scholar]
  14. C.E. Brehier, J. Cui and J. Hong, Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen—Cahn equation. IMA J. Numer. Anal. 39 (2019) 2096–2134. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Cui and J. Hong, Strong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one-sided Lipschitz coefficient. SIAM J. Numer. Anal. 57 (2019) 1815–1841. [CrossRef] [MathSciNet] [Google Scholar]
  16. C.E. Brehier and L. Goudenège, Analysis of some splitting schemes for the stochastic Allen—Cahn equation. Discrete Contin. Dyn. Syst. Ser. B 24 (2019) 4169–4190. [MathSciNet] [Google Scholar]
  17. J. Warren and S. Watanabe, On spectra of noises associated with Harris Flows.// Adv. Stud. Pure Math.. Vol. 41 of Stochastic Analysis and Related Topics in Kyoto. Math. Soc., Tokyo (2004) 351–373. [Google Scholar]
  18. H. Matsumoto, Coalescing stochastic flows on the real line. Osaka J. Math. 26 (1989) 139–158. [MathSciNet] [Google Scholar]
  19. T. Amaba, D. Taguchi and G. Yûki, Convergence implications via dual flow method. Markov Process. Related Fields 25 (2019) 533–568. [MathSciNet] [Google Scholar]
  20. M.V. Vovchanskii, Convergence of solutions of SDEs to Harris flows. Theory Stoch. Process. 23 (2018) 80–91. [MathSciNet] [Google Scholar]
  21. P. Billingsley, Convergence of Probability Measures. John Wiley & Sons, Inc., New York—London—Sydney (1968) xii+253. [Google Scholar]
  22. S.N. Ethier and T.G. Kurtz, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical statistics: Markov Processes. Characterization and Convergence. John Wiley & Sons, Inc., New York (1986) x+534. [Google Scholar]
  23. W. Whitt, Springer Series in Operations Research and Financial Engineering: Stochastic-process Limits: an Introduction to Stochastic-process Limits and their Application to Queues. Springer, New York (2002). [CrossRef] [Google Scholar]
  24. D. Ferger and D. Vogel, Weak convergence of the empirical process and the rescaled empirical distribution function in the Skorokhod product space. Teor. Veroyatn. Primen. 54 (2009) 750–770. [CrossRef] [Google Scholar]
  25. L.R.G. Fontes, M. Isopi and C.M. Newman, et al., The Brownian web: characterization and convergence. Ann. Probab. 32 (2004) 2857–2883. [MathSciNet] [Google Scholar]
  26. A.A. Dorogovtsev and M.B. Vovchanskii, Arratia flow with drift and Trotter formula for Brownian web. Commun. Stoch. Anal. 12 (2018) 89–108. [MathSciNet] [Google Scholar]
  27. I. Karatzas and S.E. Shreve, Graduate Texts in Mathematics. Vol. 113 of Brownian Motion and Stochastic Calculus, 2nd edn. Springer-Verlag, New York (1991) xxiv+470. [Google Scholar]
  28. C. Villani, Graduate studies in mathematics. Vol. 58 of Topics in Optimal Transportation. American Mathematical Society, Providence, RI (2003) xvi+370. [Google Scholar]
  29. A.A. Dorogovtsev and M.B. Vovchanskii, On the approximations of point measures associated with the Brownian web by means of the fractional step method and discretization of the initial interval. Ukrain. Math. J. 72 (2021) 1358–1376. [CrossRef] [MathSciNet] [Google Scholar]
  30. L. Szpruch and X. Zhāng, V-integrability, asymptotic stability and comparison property of explicit numerical schemes for non-linear SDEs. Math. Comp. 87 (2018) 755–783. [Google Scholar]
  31. U.S. Fjordholm, M. Musch and A. Pilipenko, The zero-noise limit of sdes with L∞ drift. (2022). [Google Scholar]
  32. S. Nakao, Comparison theorems for solutions of one-dimensional stochastic differential equations. Lecture Notes in Mathematics. Vol. 330 of Proceedings of the Second Japan-USSR Symposium on Probability Theory (Kyoto, 1972). Springer, Berlin—New York (1973) 310–315. [CrossRef] [Google Scholar]
  33. L. Yan, The Euler scheme with irregular coefficients. Ann. Probab. 30 (2002) 1172–1194. [MathSciNet] [Google Scholar]
  34. R. Adler and J. Taylor, Springer Monographs in Mathematics: Random Fields and Geometry. Springer, New York (2009) 454. [Google Scholar]
  35. O. Kallenberg, Random Measures, 3rd edn. Akademie-Verlag; Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], Berlin/London (1983) 187. [Google Scholar]
  36. G.V. Riabov, Duality for coalescing stochastic flows on the real line. Theory Stoch. Process. 23 (2018) 55–74. [MathSciNet] [Google Scholar]
  37. A.A. Dorogovtsev and V.V. Fomichov, The rate of weak convergence of the n-point motions of Harris flows. Dynam. Syst. Appl. 25 (2016) 377—392. [Google Scholar]
  38. D. Stroock and S. Varadhan, Grundlehren der mathematischen wissenschaften: Multidimensional Diffusion Processes. Springer Berlin Heidelberg (1997). [Google Scholar]
  39. R.G. Pinsky, Positive Harmonic Functions and Diffusion: An Integrated Analytic and Probabilistic Approach, Vol. 45. Cambridge University Press, Cambridge (1995) xvi + 474. [Google Scholar]
  40. L. Breiman, Classics in Applied Mathematics: Probability. Society for Industrial and Applied Mathematics (1968). [Google Scholar]
  41. A. Göing-Jaeschke and M. Yor, A survey and some generalizations of Bessel processes. Bernoulli 9 (2003) 313–349. [MathSciNet] [Google Scholar]
  42. I. Karatzas and J. Ruf, Distribution of the time to explosion for one-dimensional diffusions. Probab. Theory Related Fields, 164 (2016) 1027–1069. [CrossRef] [MathSciNet] [Google Scholar]
  43. D. Revuz and M. Yor, Grundlehren der mathematischen wissenschaften [fundamental principles of mathematical sciences]. Vol. 293 of Continuous Martingales and Brownian Motion, 3rd edn. Springer-Verlag, Berlin (1999) xiv+602. [Google Scholar]

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