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Seminar

Language	English
From	2012/03/13 13:30
To	2012/03/13 15:00
Place	127 Conference Room, Building No.3, Faculty of Science, Kyoto University
Seminar Name	Kansai Probability Theory Seminar
Title	Construction of random time with a given conditional survival probability
Field	Analysis
Speakers	Monique Jeanblanc
Affiliation	Universite d'Evry
Abstract	In this paper, we prove that, if an $\mathbb{F}$ supermartingale $Z$ valued in $[0,1]$ admits a multiplicative decomposition $Z_t=N_te^{-A_t}$ where $A$ is a continuous increasing process $A$ , one can construct (infinitely many) random times $\tau$ such that $\mathbb{P}(\tau >t \lbrace \mathcal{F}_t)= N_te^{-A_t}$ . To solve the problem, we exhibit random times admitting a conditional law with respect to $\mathbb{F}$ , i.e., $\mathbb{P}(\tau \leq u \lbrace <br>\mathcal{F}_t)=:M^u_t$ such that $M_t^t=1-Z_t$ . The difficulty is that the family of martingales $M^u$ must be increasing w.r.t. the parameter $u$ . All the random times admit $A$ as intensity, i.e., ${1\!\!1}_{\tau \leq t}-A_{t \wedge \tau}$ are martingales. http://www-an.acs.i.kyoto-u.ac.jp/~hino/probability/seminar/abstract/110313jeanblanc.pdf
Note	曜日，時間，場所がいつもと違います
Link	http://www-an.acs.i.kyoto-u.ac.jp/~hino/probability/seminar/index_j.html