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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 10, 2017

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

  • Jacek Jakubowski EMAIL logo and Maciej Wiśniewolski
From the journal Demonstratio Mathematica

Abstract

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 given Bt = 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.

MSC 2010: 60G15; 60J55

References

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Received: 2011-12-9
Published Online: 2017-5-10
Published in Print: 2012-6-1

© 2012 Jacek Jakubowski et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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