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probability-theory

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

Feb 3, 2016

(Elementary) Markov property of the Brownian motion

Jul 3, 2015

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

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

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

Jan 30, 2014

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Sequence converging to the supremum

Jun 14, 2017

$5$ questions on the definition of the Gelfand triple

Jan 10, 2016

Measurable function applied on stationary sequence

Aug 11, 2019

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

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

May 25, 2020

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How can we show that $\left(X^{(1)}_t\right)_{t\in[0,\:\tau_1)}$ and $\left(X^{(2)}_t\right)_{t\in[0,\:\tau_2)}$ are independent here?

+20

Numerical computation of the continuous Fourier transform

+10

Does $A^TA=I$ imply $AA^T=I$?

+10

Does the Helmholtz-Leray projection map $H^1$ to itself?

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Numerical computation of the continuous Fourier transform

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How can we show that $\left(X^{(1)}_t\right)_{t\in[0,\:\tau_1)}$ and $\left(X^{(2)}_t\right)_{t\in[0,\:\tau_2)}$ are independent here?

Jun 5

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