STOCHASTIC INTEGRATION WITH RESPECT TO CYLINDRICAL LEVY PROCESSES

被引：11

作者：

Jakubowski, Adam ^{[1
]}

Riedle, Markus ^{[2
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Torun, Poland

[2] Kings Coll London, Dept Math, London WC2R 2LS, England

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 6B期

基金：

英国工程与自然科学研究理事会;

关键词：

Cylindrical Levy processes; stochastic integration; decoupled tangent sequence; cylindrical Brownian motion; random measures; LIMIT-THEOREMS; BANACH-SPACES; SUMS;

D O I：

10.1214/16-AOP1164

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A cylindrical Levy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Levy processes in Hilbert spaces. The space of admissible integrands consists of caglad, adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the integrator is required to satisfy any moment or boundedness condition. The integral process is characterised as an adapted, Hilbert space valued semimartingale with cadlag trajectories.

引用

页码：4273 / 4306

页数：34

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