# Questions tagged [wiener-measure]

The wiener-measure tag has no usage guidance.

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### How far away is $\max_{x: x \in \{0, \ldots, N\}} |W(x/N)|$ from $\max_{0 \leq t \leq 1} |W(t)|$ ($W(t)$ a Wiener process)?

How far away is
$$\max_{x: x \in \{0, \ldots, N\}} \left|W\left(\frac{x}{N}\right)\right|$$
from
$$\max_{0 \leq t \leq 1} |W(t)|$$
In other words, if you simulate a Wiener process over a finite ...

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### On measurability in Wiener space

Let $f$ be a complex-valued continuous function on Wiener space such that $|f|$ is measurable. Is $f$ then measurable, too? I am looking for a proof or a counterexample.

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### Convergence of an integral with respect to the Wiener measure

Most probably this question should be well studied in the theory of stochastic processes, but I am not educated in that area. Sorry if this question is too elementary.
Let $V\colon \mathbb{R}\to \...

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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 ...

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### can I integrate product or square of a white noise in any sense?

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 ...

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### References about distances between singular probability measures

I would be interested in references on the topic of distances between probability measures that are singular with one another and not reduced to trivial ones. For example from here we know that total ...