Professional paper

Stochastic processes defined by the integral with respect to a random measure

Danijel Danijel Grahovac orcid.org/0000-0001-6918-3456 ; Odjel za matematiku, Sveučilište J. J. Strossmayera u Osi
Dominik Mihalčić orcid.org/0009-0007-1003-5767 ; Odjel za matematiku, Sveučilište J. J. Strossmayera u Osijeku

Abstract

This paper first explains the concept of infinite divisibility for random variables and processes. As a special form of stochastic process,random measures are defined and the most important examples are given. The integral with respect to a random measure is first defined or simple and then for general functions. Necessary and sufficient conditions for the integrand that ensure the integral is well defined are stated. Explicit expressions are given for the characteristic triplet of an infinitely divisible random variable defined by the integral. In the last part, examples of processes defined by the stochastic integral
and their most important properties are given.

Keywords

infinite divisibility, random measure, Lévy-Khintchine formula, Lévy processes

Hrčak ID:

310199

URI

https://hrcak.srce.hr/310199

Publication date:

10.12.2023.

Article data in other languages: croatian

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