Stochastic integration with respect to canonical α-stable cylindrical Lévy processes
نویسندگان
چکیده
In this work, we introduce a theory of stochastic integration with respect to symmetric α-stable cylindrical Lévy processes. Since processes do not enjoy semi-martingale decomposition, our approach is based on decoupling inequality for the tangent sequence Radonified increments. This enables us characterise largest space predictable Hilbert-Schmidt operator-valued which are integrable an process as collection all paths in Bochner Lα. We demonstrate power and robustness developed by establishing dominated convergence result allowing interchange integral limit.
منابع مشابه
Stochastic Integration with respect to Volterra processes
We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a timedependent kernel with respect to a standard Brownian motion. For these processes which are natural generalization of fractional Brownian motion, we construct a stochastic integral and show some of its main properties: regularity with respect to ...
متن کاملStochastic Integration with respect to Gaussian Processes
We construct a Stratonovitch-Skorohod-like stochastic integral for general Gaussian processes. We study its sample-paths regularity and one of its numerical approximating schemes. We also analyze the way it is transformed by an absolutely continuous change of probability and we give an Itô formula. c 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Intégrale stochasti...
متن کاملStochastic Integral with respect to Cylindrical Wiener Process
This paper is devoted to a construction of the stochastic Itô integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the introduced integral with the integral defined by Walsh [9] is provided as well.
متن کاملStochastic Bounds for Lévy Processes
Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrat...
متن کاملAn introduction to stochastic integration with respect to continuous semimartingales
Contents Preface v 1 Continuous-time stochastic processes 1 1.1 Measurability and stopping times. . Bibliography 133 iv CONTENTS Preface This monograph concerns itself with the theory of continuous-time martingales with continuous paths and the theory of stochastic integration with respect to continuous semimartingales. To set the scene for the theory to be developed, we consider an example. As...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2022
ISSN: ['1083-6489']
DOI: https://doi.org/10.1214/22-ejp884