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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

4 votes
1 answer
34 views

Stability of stochastic differential equations

Consider an SDE of the form $$dX^\mu_t = a(t, X^\mu_t) dt + \sigma(t, X^\mu_t) dB_t$$ with initial condition $X^\mu_0 \sim \mu$, where $\mu$ is some measure on $\mathbb{R}^d$. I am searching for stabi …
Robert Wegner's user avatar
5 votes
1 answer
134 views

Girsanov's theorem for Gaussian measures as the Cameron-martin theorem with a random shift

Let $H \subset E$ be the Cameron-Martin space of a Gaussian measure $\mu$ on a separable Banach space $E$. The Cameron-Martin theorem states that for all $h \in E$ we have $h \in H$ if and only if $\m …
Robert Wegner's user avatar