## Bernoulli

• Bernoulli
• Volume 21, Number 4 (2015), 2513-2551.

### Lévy processes and stochastic integrals in the sense of generalized convolutions

#### Abstract

In this paper, we present a comprehensive theory of generalized and weak generalized convolutions, illustrate it by a large number of examples, and discuss the related infinitely divisible distributions. We consider Lévy and additive process with respect to generalized and weak generalized convolutions as certain Markov processes, and then study stochastic integrals with respect to such processes. We introduce the representability property of weak generalized convolutions. Under this property and the related weak summability, a stochastic integral with respect to random measures related to such convolutions is constructed.

#### Article information

Source
Bernoulli, Volume 21, Number 4 (2015), 2513-2551.

Dates
Revised: March 2014
First available in Project Euclid: 5 August 2015

https://projecteuclid.org/euclid.bj/1438777603

Digital Object Identifier
doi:10.3150/14-BEJ653

Mathematical Reviews number (MathSciNet)
MR3378476

Zentralblatt MATH identifier
1333.60091

#### Citation

Borowiecka-Olszewska, M.; Jasiulis-Gołdyn, B.H.; Misiewicz, J.K.; Rosiński, J. Lévy processes and stochastic integrals in the sense of generalized convolutions. Bernoulli 21 (2015), no. 4, 2513--2551. doi:10.3150/14-BEJ653. https://projecteuclid.org/euclid.bj/1438777603

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