Open Access
Issue
ESAIM: PS
Volume 30, 2026
Page(s) 372 - 409
DOI https://doi.org/10.1051/ps/2026006
Published online 16 July 2026
  1. Y. Kutoyants, Statistical Inference for Ergodic Diffusion Processes. Springer London (2004). [Google Scholar]
  2. S. Ditlevsen and A. Samson, Parameter estimation in neuronal stochastic differential equation models from intracellular recordings of membrane potentials in single neurons: a Review. J. Soc. Française Statist. 157 (2016) 6–21. [Google Scholar]
  3. A. Delporte, S. Ditlevsen and A. Samson, Varying coefficients correlated velocity models in complex landscapes with boundaries applied to narwhal responses to noise exposure. Ann. Appl. Stat. 19 (2025) 2898–2917. [Google Scholar]
  4. D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance. CRC Press, New York (2011). [Google Scholar]
  5. F. Black and M. Fischer, The pricing of options and corporate liabilities. J. Pol. Econ. 81 (1973) 637–654. [Google Scholar]
  6. N. Marie, Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models. Finance Stochast. 27 (2023) 97–126. [Google Scholar]
  7. Y. Aït-Sahalia, D. Amengual and E. Manresa, Market-based estimation of stochastic volatility models. J. Econom. 187 (2015) 418-435 [Google Scholar]
  8. A. Dalalyan, Sharp adaptive estimation of the drift function for ergodic diffusions. Ann. Statist. 33 (2005) 2507–2528. [Google Scholar]
  9. J.O. Ramsay and B.W. Silverman, Applied Functional Data Analysis: Methods and Case Studies. Springer, New York (2007). [Google Scholar]
  10. J.-L. Wang, J.-M. Chiou and H.-G. Mueller, Functional data analysis. Annu. Rev. Statist. Appl. 3 (2016) 257–295. [Google Scholar]
  11. F. Comte and V. Genon-Catalot, Regression function estimation as a partly inverse problem. Ann. Inst. Statist. Math. 72 (2019) 1023–1054. [Google Scholar]
  12. C. Denis, C. Dion-Blanc and M. Martinez, A ridge estimator of the drift from discrete repeated observations of the solution of a stochastic differential equation. Bernoulli 27 (2021) 2675–2713. [Google Scholar]
  13. N. Marie and A. Rosier, Nadaraya–Watson estimator for I.I.D. paths of diffusion processes. Scand. J. Statist. 50 (2023) 589–637. [Google Scholar]
  14. E. Ella-Mintsa, Nonparametric estimation of the diffusion coefficient from i.i.d. S.D.E. paths. Statist. Inference Stoch. Processes 27 (2024) 585–640. [Google Scholar]
  15. C. Denis, C. Dion and M. Martinez, Consistent procedures for multiclass classification of discrete diffusion paths. Scand. J. Statist. 47 (2019) 516–554. [Google Scholar]
  16. L. Della Maestra and M. Hoffmann, Nonparametric estimation for interacting particle systems: McKean–Vlasov models. Probab. Theory Related Fields 182 (2022) 551–613. [Google Scholar]
  17. D. Belomestny, V. Pilipauskaité and M. Podolskij, Semiparametric estimation of McKean–Vlasov SDEs. Ann. Inst. Henri Poincaré Probab. Statist. 59 (2023) 79–96. [Google Scholar]
  18. C. Amorino, A. Heidari, V. Pilipauskaite and M. Podolskij, Parameter estimation of discretely observed interacting particle systems. Stoch. Processes Appl. 163 (2023) 350–386. [Google Scholar]
  19. C. Amorino, D. Belomestny, V. Pilipauskaite, M. Podolskij and S. Zhou, Polynomial rates via deconvolution for nonparametric estimation in McKean–Vlasov SDEs. Probab. Theory Relat. Fields 193 (2025) 539–584. [Google Scholar]
  20. G. Milstein and J. Schoenmakers, Transition density estimation for stochastic differential equations via forward-reverse representations. Bernoulli 10 (2004) 281–312. [Google Scholar]
  21. F. Comte and N. Marie, Nonparametric estimation of the transition density function for diffusion processes. Stoch. Processes Appl. 188 (2025) 104667. [Google Scholar]
  22. N. Marie and O. Sacko, Nadaraya–Watson type estimator of the transition density function for diffusion processes. Ann. Inst. Statist. Math. (2026) to appear. [Google Scholar]
  23. C. Lacour, Adaptive estimation of the transition density of a Markov chain. Ann. Inst. Henri Poincare Probab. Statist. 43 (2007) 571–597. [Google Scholar]
  24. C. Lacour, Nonparametric estimation of the stationary density and the transition density of a Markov chain. Stoch. Processes Appl. 118 (2008) 232–260. [Google Scholar]
  25. M. Sart, Estimation of the transition density of a Markov chain. Ann. Inst. Henri Poincare Probab. Statist. 50 (2014) 1028–1068. [Google Scholar]
  26. M. Mollenhauer and P. Koltai, Nonparametric approximation of conditional expectation operators. (2023) Preprint arXiv:2012.12917. [Google Scholar]
  27. L. Song, J. Huang, A. Smola and K. Fukumizu, Hilbert space embeddings of conditional distributions with applications to dynamical systems. Proceedings of the 26th Annual International Conference on Machine Learning. (2009) 961–968. [Google Scholar]
  28. K. Muandet, K. Fukumizu, B. Sriperumbudur and B. Schölkopf, Kernel mean embedding of distributions: a review and beyond. Found. Trends Mach. Learn. 10 (2017) 1–141. [Google Scholar]
  29. Y. Aït-Sahalia, Transition densities for interest rate and other nonlinear diffusions. J. Finance 54 (2002) 1361–1395. [Google Scholar]
  30. S. Grünewälder, G. Lever, L. Baldassarre, S. Patterson, A. Gretton and M. Pontil, Conditional mean embeddings as regressors. (2012) Preprint arXiv:1205.4656. [Google Scholar]
  31. F. Comte and V. Genon-Catalot, Nonparametric drift estimation for i.i.d. paths of stochastic differential equations. Ann. Statist. 48 (2020) 3336–3365. [Google Scholar]
  32. A. Cohen, M. Davenport and D. Leviatan, On the stability and accuracy of least squares approximations. Found. Computat. Math. 13 (2013) 819–834. [Google Scholar]
  33. E. Brunel, F. Comte and C. Lacour, Minimax estimation of the conditional cumulative distribution function. Sankhya A 72 (2010) 293–330. [Google Scholar]
  34. F. Comte, Nonparametric Estimation. Spartacus-Idh (2017). [Google Scholar]
  35. F. Comte and C. Lacour, Non-compact estimation of the conditional density from direct or noisy data. Ann. Inst. Henri Poincaré Probab. Statist. 59 (2023) 1463–1507. [Google Scholar]
  36. G. Leonenko and T. Phillips, High-order approximation of Pearson diffusion processes. J. Computat. Appl. Math. 236 (2012) 2853–2868. [Google Scholar]
  37. J. Baudry, C. Maugis and B. Michel, Slope heuristics: overview and implementation. Statist. Comput. 22 (2012) 455–470. [Google Scholar]
  38. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, USA (1964). [Google Scholar]
  39. S. Efromovich, Nonparametric Curve Estimation. Springer, New York (1999). [Google Scholar]
  40. Y. Aït-Sahalia and J. Duarte, Nonparametric option pricing under shape restrictions. J. Econom. 116 (2003) 9–47. [Google Scholar]
  41. S. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. 6 (1993) 327–343. [Google Scholar]
  42. M. Rubinstein, Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE option classes from August 23, 1976 through August 31, 1978. J. Finance 40 (1985) 455–480. [Google Scholar]
  43. F. Dussap, Nonparametric multiple regression by projection on non-compactly supported bases. Ann. Inst. Statist. Math. 75 (2023)) 731–771. [Google Scholar]
  44. S. Menozzi, A. Pesce and X. Zhang, Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. J. Diff. Equ. 272 (2021) 330–369. [Google Scholar]
  45. A. Tsybakov, Introduction to Nonparametric Estimation. Springer, New York (2009). [Google Scholar]
  46. Y. Huang, Non-compactly supported estimation of the diffusion function in ergodic scalar SDEs. (2025) Preprint hal-04901917v3. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.