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0xbadf00d
  • Member for 11 years, 8 months
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  • Germany
45 votes
4 answers
12k views

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

20 votes
1 answer
7k views

(Elementary) Markov property of the Brownian motion

18 votes
3 answers
1k views

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

17 votes
0 answers
403 views

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

15 votes
2 answers
6k views

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

14 votes
1 answer
2k views

Why is a predictable stochastic process called *predictable*?

14 votes
2 answers
2k views

$5$ questions on the definition of the Gelfand triple

13 votes
2 answers
2k views

If $f∈C^1$ and $\{∇f=0\}$ has Lebesgue measure $0$, then $\{f∈B\}$ has Lebesgue measure $0$ for all Borel measurable $B⊆ℝ$ with Lebesgue measure $0$

12 votes
4 answers
11k views

Laplacian of a radial function

9 votes
2 answers
517 views

If $h$ is twice differentiable, then $|h|$ is twice differentiable except on a countable set

9 votes
3 answers
1k views

Is there a version of the Arzelà–Ascoli theorem capturing $C([0,\infty))$?

9 votes
2 answers
426 views

If $Y\sim\mu$ with probability $p$ and $Y\sim\kappa(X,\;\cdot\;)$ otherwise, what's the conditional distribution of $Y$ given $X$?

8 votes
1 answer
315 views

If $X^{(n)},X$ are càdlàg and $X^{(n)}\to X$ in distribution, do the corresponding transition semigroups strongly converge?

8 votes
1 answer
1k views

Convergence of the distribution of the Langevin diffusion to its invariant measure

8 votes
1 answer
89 views

$A:=\left\{y\in\mathbb{R}:\mu\left(f^{-1}(\left\{y\right\})\right)>0\right\}$ is countable, if $\mu$ is a finite measure and $f$ has compact support

8 votes
4 answers
2k views

What did Johann Bernoulli wrong in his proof of $\ln z=\ln (-z)$?

8 votes
0 answers
203 views

Recast the scalar SPDE $du_t(Φ_t(x))=f_t(Φ_t(x))dt+∇ u_t(Φ_t(x))⋅ξ_t(Φ_t(x))dW_t$ into a SDE in an infinite dimensional function space.

8 votes
2 answers
184 views

When is an operator $T$ on $L^1(\mu)$ of the form $(Tf)(x)=\int\mu({\rm d}y)p(x,y)f(y)$?

8 votes
0 answers
108 views

Show convergence of measure of a sequence of sets

7 votes
1 answer
263 views

Convolution of tight measures is tight

7 votes
1 answer
341 views

Can we apply an Itō formula to find an expression for $f(t,X_t)$, if $f$ is taking values in a Hilbert space?

7 votes
0 answers
328 views

Derivation of a stochastic Navier-Stokes equation with multiplicative noise

7 votes
1 answer
7k views

Natural matrix norm of an inverse matrix

7 votes
3 answers
8k views

Why is the reciprocal of an $n$-th root of unity its complex conjugate?

7 votes
2 answers
13k views

Finding all basic feasible solutions in a linear program

7 votes
2 answers
420 views

How to prove $\int_0^\infty e^{-x}\frac{\sin^2 x}{x}\text{ dx}=\frac{\text{log }5}{4}$

7 votes
1 answer
3k views

What is the distribution of a stochastic process?

7 votes
0 answers
166 views

Implementation of a simulation of an incompressible Newtonian fluid with uniform density

7 votes
2 answers
5k views

Prove that $X,Y$ are independent iff the characteristic function of $(X,Y)$ equals the product of the characteristic functions of $X$ and $Y$

7 votes
1 answer
336 views

If $\mu$ has a density with respect to the Lebesgue measure, is $C_c(\mathbb R)$ dense in $L^p(\mu)$?

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