# Questions tagged [wiener-measure]

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### Functional integral formulas for the wave equation and other hyperbolic PDEs

The Feynman–Kac formula provides a functional (Wiener) integral representation of the solution $u$ to the heat equation \begin{align*} \partial_t u &= \frac{1}{2}\Delta_x u,\\ u(0,x) &= ...
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### Abstract Wiener spaces for pinned processes (e.g., Brownian Bridge)

In introductions to abstract Wiener spaces, the sample paths usually form a Banach space; so, in particular, the sum of two sample paths is a valid sample path and also an element of the Banach space. ...
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### How does the conditional Wiener measure work?

In the theorem below $P_D$ means the heat kernel in the open $D \subset \mathbb{R}^m$ and $P_m$ is the heat kernel in whole $\mathbb{R}^m.$ I know absolutely nothing about what Brownian bridges are, ...
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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 ...
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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 ...