Accuracy of discrete approximation for integral functionals of Markov processes
Volume 2, Issue 4 (2015), pp. 401–420
Pub. online: 30 December 2015
Type: Research Article
Open Access
Received
4 December 2015
4 December 2015
Revised
15 December 2015
15 December 2015
Accepted
15 December 2015
15 December 2015
Published
30 December 2015
30 December 2015
Abstract
The article is devoted to the estimation of the convergence rate of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density differentiable in t and the derivative has an integrable upper bound of a certain type, we derive the accuracy rates for strong and weak approximations of the functionals by Riemannian sums. We also develop a version of the parametrix method, which provides the required upper bound for the derivative of the transition probability density for a solution of an SDE driven by a locally stable process. As an application, we give accuracy bounds for an approximation of the price of an occupation time option.
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