2026-04-14T06:11:33Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1248352025-12-05T09:54:22Zcom_2072_1057col_2072_478917col_2072_478920

Anticipative integrals with respect to a filtered Lévy process and Lévy-Itô decomposition Savy, Nicolas Vives i Santa Eulàlia, Josep, 1963- Anàlisi estocàstica Processos estocàstics Analyse stochastique Stochastic processes A filtered process $X^k$ is defined as an integral of a deterministic kernel $k$ with respect to a stochastic process $X$. One of the main problems to deal with such processes is to define a stochastic integral with respect to them. When $X$ is a Brownian motion one can use the Gaussian properties of $X^k$ to define an integral intrinsically. When $X$ is a jump process or a Levy process, this is not possible. Alternatively, we can use the integrals defined by means of the so called $\mathcal{S}$-transform or by means of the integral with respect to the process $X$ and a linear operator $\mathcal{K}$ constructed from $k$. The usual fact that even for predictable $Y$, $K^{\ast}(Y)$ may not be predictable forces us to consider only anticipative integrals. The aim of this paper is, on the one hand, to clarify the links between these integrals for a given $X$ and on the other hand, to investigate how the Lévy-Itô decomposition of a Levy process $L$, roughly speaking $L=B+J$, where $B$ is a Brownian motion and $J$ is a pure jump Lévy process, behaves with respect to these integrals. 2018-09-26T11:54:23Z 2018-09-26T11:54:23Z 2017-01 2018-09-26T11:54:23Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 0973-9599 https://hdl.handle.net/2445/124835 675812 eng Reproducció del document publicat a: https://www.math.lsu.edu/cosa/11-1-05[543].pdf Communications on Stochastic Analysis, 2017, vol. 11, num. 1, p. 63-85 (c) Serials Publications, 2017 info:eu-repo/semantics/openAccess 23 p. application/pdf Serials Publications Articles publicats en revistes (Matemàtiques i Informàtica)