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

• Autorzy: Jakubowski, J. , Wiśniewolski, M.
• Języki publikacji: EN

Abstrakty

EN

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 (…), 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.

Słowa kluczowe

EN

Brownian motion; Girsanov theorem

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 2
• Strony: 257-263
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Jakubowski, J.

autor

Wiśniewolski, M.

• Jacek Jakubowski Institute Of Mathematics University Of Warsaw Banacha 2 02 097 Warszawa, Poland,

Bibliografia

• [1] A.Borodin, P.Salminen, Handbook of Brownian Motion - Facts and Formulae Birkhauser (2nd ed.), 2002.
• [2] C.Donati Martin, M.Yor, Some Brownian functionals and their laws Ann.Probab. 25 (1997), 1011–1058.
• [3] J.Jakubowski, M.Wiśniewolski, On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models Preprint (2010).
• [4] I.Karatzas, S.Shreve, Brownian Motion and Stochastic Calculus Springer Verlag, 1991.
• [5] R.Mansuy, M.Yor, Aspects of Brownian Motion Universitext, Springer Verlag, 2008.
• [6] D.Revuz, M.Yor, Continous Martingales and Brownian Motion Springer Verlag (3rd ed.), 2005.