Conditionally Gaussian stochastic integrals

被引：1

作者：

Privault, Nicolas ^{[1
]}

She, Qihao ^{[1
]}

机构：

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

COMPTES RENDUS MATHEMATIQUE | 2015年 / 353卷 / 12期

关键词：

Quadratic Brownian functionals; Multidimensional Brownian motion; Moment identities; Characteristic functions;

D O I：

10.1016/j.crma.2015.09.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive conditional Gaussian type identities of the form E [exp (i(T)integral(0) u(t)dBt)vertical bar(T)integral(0) vertical bar u(t)vertical bar(2)dt] = exp (-1/2 (T)integral(0) vertical bar u(t)vertical bar(2) dt) for Brownian stochastic integrals, under conditions on the process (u(t))(t is an element of[0,T]) specified using the Malliavin calculus. This applies in particular to the quadratic Brownian integral integral(t)(0) AB(s)dB(s) under the matrix condition A dagger A(2) = 0, using a characterization of Yor [6]. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：1153 / 1158

页数：6

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