Time-dependent weak rate of convergence for functions of generalized bounded variation
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
Published inStochastic Analysis and Applications
© 2020 The Author(s). Published with license by Taylor and Francis Group, LLC
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.
PublisherTaylor & Francis
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Additional information about fundingThe author was financially supported by the Magnus Ehrnrooth Foundation and The FinnishCultural Foundation during the preparation of this article.
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