Weak approximation rates for integral functionals of Markov processes

TL;DR

This paper establishes weak approximation rates for integral functionals of Markov processes using transition densities, with applications to Feynman–Kac semigroups and occupation-time options pricing.

Contribution

It introduces a process-structure-independent approach for weak approximation rates based solely on transition probability densities.

Findings

Derived weak approximation rates for integral functionals

Applied results to Feynman–Kac semigroup estimates

Provided bounds for occupation-time options pricing

Abstract

We obtain weak rates for approximation of an integral functional of a Markov process by integral sums. An assumption on the process is formulated only in terms of its transition probability density, and, therefore, our approach is not strongly dependent on the structure of the process. Applications to the estimates of the rates of approximation of the Feynman--Kac semigroup and of the price of "occupation-time options" are provided.