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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.

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.

For a (non-symmetric) strong Markov process X, consider the Feynman–Kac semigroup where A is a continuous additive functional of X associated with some signed measure. Under the assumption that X admits a transition probability density that possesses upper and lower bounds of certain type, we show that the kernel corresponding to ${T_{t}^{A}}$ possesses the density ${p_{t}^{A}}(x,y)$ with respect to the Lebesgue measure and construct upper and lower bounds for ${p_{t}^{A}}(x,y)$. Some examples are provided.

For a (non-symmetric) strong Markov process X, consider the Feynman–Kac semigroup where A is a continuous additive functional of X associated with some signed measure. Under the assumption that X admits a transition probability density that possesses upper and lower bounds of certain type, we show that the kernel corresponding to ${T_{t}^{A}}$ possesses the density ${p_{t}^{A}}(x,y)$ with respect to the Lebesgue measure and construct upper and lower bounds for ${p_{t}^{A}}(x,y)$. Some examples are provided.