L\'{e}vy 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 L\'{e}vy 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.
Keywords
Cite
@article{arxiv.1312.4083,
title = {L\'{e}vy processes and stochastic integrals in the sense of generalized convolutions},
author = {M. Borowiecka-Olszewska and B. H. Jasiulis-Gołdyn and J. K. Misiewicz and J. Rosiński},
journal= {arXiv preprint arXiv:1312.4083},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ653 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)