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


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

Last updated on 2022-20-09 at 13:14