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 editorsLuoto, Antti

Journal or seriesStochastic Analysis and Applications

ISSN0736-2994

eISSN1532-9356

Publication year2021

Publication date27/08/2020

Volume39

Issue number3

Pages range494-524

PublisherTaylor & Francis

Publication countryUnited States

Publication languageEnglish

DOIhttps://doi.org/10.1080/07362994.2020.1809458

Publication open accessOpenly available

Publication channel open accessPartially open access channel

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/71715

Publication is parallel publishedhttps://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.


Keywordspartial differential equationsnumerical analysisapproximationstochastic processes

Free keywordsApproximation using simple random walk; weak rate of convergence; finite difference approximation of the heat equation


Contributing organizations


Ministry reportingYes

Reporting Year2021

JUFO rating1


Last updated on 2024-26-03 at 20:56