L\'{e}vy processes and stochastic integrals in the sense of generalized convolutions

Autor:	B. H. Jasiulis-Gołdyn, Marta Borowiecka-Olszewska, J. K. Misiewicz, Jan Rosiński
Jazyk:	angličtina
Rok vydání:	2013
Předmět:	Statistics and Probability Pure mathematics Property (philosophy) stochastic integral Lévy process Markov process scale mixture Stochastic integral Additive process symbols.namesake symbols weakly stable distribution Mathematics - Probability Mathematics symmetric stable distribution
Zdroj:	Bernoulli 21, no. 4 (2015), 2513-2551
Popis:	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. Comment: 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)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a008d271695a60d1edaf63129b60d4f http://arxiv.org/abs/1312.4083 Zobrazit plný text záznamu