Random potentials for Markov processes

Abstract

The paper is devoted to the integral functionals ${\int }_0^{\infty }f(X_t)\mathrm{d}t$ of Markov processes in $\X$ in the case $d\ge 3$. It is established that such functionals can be presented as the integrals $\int_{\X} f(y) \G(x, \mathrm{d}y, ω)$ with vector valued random measure $\G(x, \mathrm{d}y, ω)$. Some examples such as compound Poisson processes, Brownian motion and diffusions are considered.

arXiv comment12 pages. arXiv admin note: text overlap with arXiv:2006.07514

References in corpus (3)

• Point-wise estimates for nonlocal heat kernel of convolution type operators
• Perpetual Integral Functionals of Multidimensional Stochastic Processes
• Green Measures for Markov Processes