Open Access
Issue
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
Page(s) 2301 - 2318
DOI https://doi.org/10.1051/m2an/2023042
Published online 03 July 2023
  1. L. Angeli, S. Grosskinsky, A.M. Johansen and A. Pizzoferrato, Rare event simulation for stochastic dynamics in continuous time. J. Stat. Phys. 176 (2019) 1185–1210. [Google Scholar]
  2. G. Barles and E.R. Jakobsen, Error bounds for monotone approximation schemes for parabolic Hamilton–Jacobi–Bellman equations. Math. Comput. 76 (2007) 1861–1893. [CrossRef] [Google Scholar]
  3. G. Barles and E.R. Jakobsen, On the convergence rate of approximation schemes for Hamilton–Jacobi–Bellman equations. ESAIM: Math. Model. Numer. Anal. 36 (2002) 33–54. [CrossRef] [EDP Sciences] [Google Scholar]
  4. A.N. Borodin and P. Salminen, Handbook of Brownian Motion-Facts and formulae. Springer Science and Business Media. Springer-Verlag, New York (2015). [Google Scholar]
  5. J. Bucklew, Introduction to rare event simulation, in Springer Series in Statistics, Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  6. M.G. Crandall and P.-L. Lions, Two approximations of solutions of Hamilton-Jacobi equations. Math. Comput. 43 (1984) 1–19. [CrossRef] [Google Scholar]
  7. P. Del Moral, Feynman-Kac Formulae. Probability and its Applications. Springer (2004). [CrossRef] [Google Scholar]
  8. P. Dupuis and H. Wang, Subsolutions of an Isaacs equation and efficient schemes for importance sampling. Math. Oper. Res. 32 (2007) 723–757. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Dupuis, A.D. Sezer and H. Wang, Dynamic importance sampling for queueing networks. Ann. Appl. Prob. 17 (2007) 1306–1346. [CrossRef] [Google Scholar]
  10. L.C. Evans, Partial differential equations, in Graduate Studies in Mathematics. Vol. 19. American Mathematical Society (2010). [CrossRef] [Google Scholar]
  11. W.E,J. Han and A. Jentzen, Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Comm. Math. Stat. 5 (2017) 349–380. [CrossRef] [Google Scholar]
  12. G. Ferré and T. Grafke, Approximate optimal controls via instanton expansion for low temperature free energy computation. SIAM Multiscale Model. Simul. 19 (2021) 1310–1332. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Ferré and G. Stoltz, Error estimates on ergodic properties of discretized Feynman-Kac semigroups. Numer. Math. 143 (2019) 261–313. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Ferré and G. Stoltz, Large deviations of empirical measures of diffusions in weighted topologies. Electron. J. Prob. 25 (2020) 1–52. [Google Scholar]
  15. W.H. Fleming, Exit probabilities and optimal stochastic control. Appl. Math. Optim. 4 (1977) 329–346. [Google Scholar]
  16. W.H. Fleming and M.R. James, Asymptotic series and exit time probabilities. Ann. Probab. 20 (1992) 1369–1384. [CrossRef] [MathSciNet] [Google Scholar]
  17. W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions, in Stochastic Modelling and Applied Probability. Vol. 25. Springer Science & Business Media (2006). [Google Scholar]
  18. M.I. Freidlin and A.D. Wentzell, Random perturbations of dynamical systems, in Grundlehren der mathematischen Wissenschaften. Vol. 260. Springer (1998). [CrossRef] [Google Scholar]
  19. P. Glasserman and Y. Wang, Counterexamples in importance sampling for large deviations probabilities. Ann. Appl. Probab. 7 (1997) 731–746. [CrossRef] [MathSciNet] [Google Scholar]
  20. T. Grafke and E. Vanden-Eijnden, Numerical computation of rare events via large deviation theory. Chaos 29 (2019) 063118. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. A. Guyader and H. Touchette, Efficient large deviation estimation based on importance sampling. J. Stat. Phys. 181 (2020) 551–586. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Hairer and J. Weare, Improved diffusion Monte Carlo. Comm. Pure Appl. Math. 67 (2014) 1995–2021. [CrossRef] [MathSciNet] [Google Scholar]
  23. C. Hartmann and C. Schütte, Efficient rare event simulation by optimal nonequilibrium forcing. J. Stat. Mech. Theory Exp. 2012 (2012) 11004. [Google Scholar]
  24. I. Karatzas and S. Shreve, Brownian motion and stochastic calculus, in Graduate Texts in Mathematics. vol. 113. Springer Science & Business Media (2012). [Google Scholar]
  25. T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics. Acta Numer. 25 (2016) 681–880. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Léonard, Feynman-Kac formula under a finite entropy condition. Preprint arXiv:2104.09171 (2021). [Google Scholar]
  27. A.M. Oberman, Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton-Jacobi equations and free boundary problems. SIAM J. Numer. Anal. 44 (2006) 879–895. [CrossRef] [MathSciNet] [Google Scholar]
  28. H. Pham, Continuous-time stochastic control and optimization with financial applications, in Stochastic Modelling and Applied Probability. Vol. 61. Springer Science & Business Media (2009). [CrossRef] [Google Scholar]
  29. L. Rey-Bellet, Ergodic properties of Markov processes, in Open Quantum Systems II. Springer (2006) 1–39. [Google Scholar]
  30. P.E. Souganidis, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Differ. Equ. 59 (1985) 1–43. [Google Scholar]
  31. E. Vanden-Eijnden and J. Weare, Rare event simulation of small noise diffusions. Comm. Pure Appl. Math. 65 (2012) 1770–1803. [CrossRef] [MathSciNet] [Google Scholar]
  32. W. Zhang, H. Wang, C. Hartmann, M. Weber and C. Schütte, Applications of the cross-entropy method to importance sampling and optimal control of diffusions. SIAM J. Sci. Comput. 36 (2014) A2654–A2672. [CrossRef] [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.

Recommended for you