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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 14
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Articles

Random potentials for Markov processes

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Pages 3874-3885 | Received 01 Aug 2020, Accepted 09 Jul 2022, Published online: 16 Jul 2022
 

Abstract

This paper is devoted to the integral functionals 0f(Xt)dt of Markov processes in Rd in the case d3. It is established that such functionals can be presented as the integrals Rdf(y)G(x,dy,ω) with vector valued random measure G(x,dy,ω). Some examples such as compound Poisson processes, Brownian motion and diffusions are considered.

AMS Subject Classifications 2010:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been partially supported by Center for Research in Mathematics and Applications (CIMA) related with the Statistics, Stochastic Processes and Applications (SSPA) group, through the grant [UIDB/MAT/04674/2020] of FCT-Fundação para a Ciência e a Tecnologia, Portugal. The financial support by the Ministry for Science and Education of Ukraine through Project [0119U002583] is gratefully acknowledged.

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