English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 S-transform or by means of the integral with respect to the process X and a linear operator K constructed from k. The usual fact that even for predictable Y , K * (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 Levy–Ito decomposition of a Levy process L, roughly speaking L = B + J, where Bis a Brownian motion and J is a pure jump Levy process, behaves with respect to these integrals.

Anticipative Integrals with Respect to a Filtered Lévy Process and Lévy–Itô Decomposition