Time-dependent weak rate of convergence for functions of generalized bounded variation
Year of publication
2021
Authors
Luoto, Antti
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.
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Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Publisher
Volume
39
Issue
3
Pages
494-524
ISSN
Publication forum
Publication forum level
1
Open access
Open access in the publisher’s service
Yes
Open access of publication channel
Partially open publication channel
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object],[object Object]
Publication country
United States
Internationality of the publisher
International
Language
English
International co-publication
No
Co-publication with a company
No
DOI
10.1080/07362994.2020.1809458
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes