A1 Journal article (refereed)
Time-dependent weak rate of convergence for functions of generalized bounded variation (2021)
Luoto, A. (2021). Time-dependent weak rate of convergence for functions of generalized bounded variation. Stochastic Analysis and Applications, 39(3), 494-524. https://doi.org/10.1080/07362994.2020.1809458
JYU authors or editors
Publication details
All authors or editors: Luoto, Antti
Journal or series: Stochastic Analysis and Applications
ISSN: 0736-2994
eISSN: 1532-9356
Publication year: 2021
Publication date: 27/08/2020
Volume: 39
Issue number: 3
Pages range: 494-524
Publisher: Taylor & Francis
Publication country: United States
Publication language: English
DOI: https://doi.org/10.1080/07362994.2020.1809458
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71715
Publication is parallel published: https://arxiv.org/abs/1609.05768
Abstract
Let W denote the Brownian motion. For any exponentially bounded Borel function g the function u defined by u(t,x)=E[g(x+σWT−t)] is the stochastic solution of the backward heat equation with terminal condition g. Let un(t,x) denote the corresponding approximation generated by a simple symmetric random walk with time steps 2T/n and space steps ±σ√T/n where σ>0. For a class of terminal functions g having bounded variation on compact intervals, the rate of convergence of un(t,x) to u(t, x) is considered, and also the behavior of the error un(t,x)−u(t,x) as t tends to T.
Keywords: partial differential equations; numerical analysis; approximation; stochastic processes
Free keywords: Approximation using simple random walk; weak rate of convergence; finite difference approximation of the heat equation
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 1