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# Questions tagged [wiener-measure]

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### Wiener Measure measure on functions?

I know that the Wiener measure for the Brownian motion $\{B_t\}_{t\ge 0}$ on the probability space $(\Omega, \mathscr{F},P)$ can be defined as $\mu=P\circ B^{-1}$ acting on the sigma-algebra generated ...
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### interpretation of the transition probability of a brownian motion in terms of the Wiener measure

Let $W(t)$ be a standard brownian motion in $E \triangleq \mathbb{R}^d$. The transition probability from a state $x \in E$ at time $t$ to a state $y \in E$ at time $T$ is  p(x,t;y,T) = \frac{1}{\...
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### Conditional Wiener measure continuous

consider a complete Riemannian manifold $M$ with heat kernel $p_M$ and let $U\subset M$ be an open set. Let $W_{x,t}^{y}$ be the Wiener measure associated to the Brownian motion starting at $x$ and ...
Assume that we have $\epsilon_1, \; \epsilon_2$ independent white noises. Can I write $\int_{0}^1 \epsilon_1^2(t)dt$ Can I write $\int_{0}^1 \epsilon_1(t) \epsilon_2(t)dt$ 1 and 2 obviously make no ...