Conditional version of the Donati-Martin and Yor formula and its applications

Demonstratio mathematica

article

Jacek Jakubowski¹  Maciej Wiśniewolski¹ 

[1] Institute of Mathematics, University of Warsaw, Poland and Faculty of Mathematics and Information Science, Warsaw University of Technology

关键词: Brownian motion;    conditional functional of Brownian motion;    Girsanov theorem;   

DOI  :  10.1515/dema-2013-0380

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

We present a new elementary and elegant probabilistic proof of conditional version of the Donati-Martin and Yor formula, more precisely, the conditional version of the Laplace transform of ∫0tBu2du$\int_0^t {B_u^2 du} $ given B t = y , where B is a Brownian motion. Next, using our form of conditional formula, we obtain the new results concerning Laplace transforms of some processes and a kind of reflection principle.

【 授权许可】

CC BY