# ESTIMATES IN EXIT PROBABILITY FOR SOLUTIONS OF NUCLEAR SPACE-VALUED SDE

• Published : 2001.02.01

#### Abstract

We consider a solution process of stochastic differential equation(SDE) driven by S'($R^d$)-valued Wiener process and study a large deviation type of estimates for the process. We get an upper bound in exit probability for such a process to leave a ball of radius $\tau$ before a finite time t. We apply the Ito formula to the SDE under the structure of nuclear space.

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