Approximation of heat equation and backward SDEs using random walk : convergence rates
This thesis addresses questions related to approximation arising from the ﬁelds of stochastic analysis and partial diﬀerential equations. Theoretical results regarding convergence rates are obtained by using discretization schemes where the limiting process,
the Brownian motion, is approximated by a simple discretetime random walk.
The rate of convergence is derived for a ﬁnitediﬀerence approximation of the solution
of a terminal value problem for the backward heat equation. This weak approximation
result is proved for a terminal function which has bounded variation on compact sets.
The sharpness of the according rate is achieved by applying some new results related to
the ﬁrst exit time behavior of Brownian bridges. In addition, convergence rates in the
L2norm are proved for Markovian forwardbackward stochastic diﬀerential equations,
where the underlying forward process is either Brownian motion or a more general Itô
diﬀusion.
Publisher
University of JyväskyläISBN
9789513975760ISSN Search the Publication Forum
14578905Keywords
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