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probability-theory

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40

What is "white noise" and how is it related to the Brownian motion?

Feb 3, 2016

20

(Elementary) Markov property of the Brownian motion

Jul 3, 2015

18

If $A$ is positive definite, then $\int_{\mathbb{R}^n}\mathrm{e}^{-\langle Ax,x\rangle}\text{d}x=\left|\det\left({\pi}^{-1}A\right)\right|^{-1/2}$

Jan 27, 2014

17

If $X_i∼fλ$, $Z∼\mathcal N(0,I_d)$ and $Y=X+\ell d^{-α}Z$ with $α<1/2$, then $\liminf_{d→∞}\text E\left[1∧\prod_{i=1}^d\frac{f(Y_i)}{f(X_i)}\right]=0$

Mar 8, 2019

15

When is the automorphism group $\text{Aut }G$ cyclic?

Jan 30, 2014

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9

Sequence converging to the supremum

Jun 14, 2017

6

Measurable function applied on stationary sequence

Aug 11, 2019

5

$5$ questions on the definition of the Gelfand triple

Jan 10, 2016

4

How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?

May 25, 2020

4

If $A$ is self-adjoint, then $\left\|A\right\|=\sup_{x\in H\setminus\{0\}}\frac{\langle Ax,x\rangle}{\left\|x\right\|^2}$

Nov 12, 2019

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probability-theory

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functional-analysis

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530

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stochastic-processes

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317

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operator-theory

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281

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measure-theory

15

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545

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+20

numerical integration of a function satisfying a ode

+10

Sequence converging to the supremum

+20

Show that the total variation distance of probability measures $\mu,\nu$ is equal to $\frac{1}{2}\sup_f\left|\int f\:{\rm d}(\nu-\mu)\right|$

+10

What is "white noise" and how is it related to the Brownian motion?

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