User 0xbadf00d

9 votes

Sequence converging to the supremum

answered Jun 14, 2017 at 20:26

6 votes

Measurable function applied on stationary sequence

answered Aug 11, 2019 at 12:30

5 votes

Accepted

$5$ questions on the definition of the Gelfand triple

answered Jan 10, 2016 at 12:20

4 votes

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

answered May 25, 2020 at 18:49

4 votes

Accepted

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

answered Nov 12, 2019 at 6:06

3 votes

Accepted

homeomorphisms mapping interiors to interiors and boundaries to boundaries

answered Aug 11, 2020 at 19:22

3 votes

Definition of relative (sequential) compactness

answered May 17, 2019 at 6:09

3 votes

Accepted

Processes $(X_t)_{t≥0}$ and $(Y_t)_{t≥0}$ are independent iff $(X_t)_{t∈I}$ and $(Y_t)_{t∈J}$ are independent for all finite $I,J⊆[0,∞)$

answered Feb 14, 2016 at 17:45

3 votes

Accepted

Abstract idea behind the method of characteristics to solve first-order PDEs

answered Apr 20, 2021 at 5:04

2 votes

Accepted

Is the symmetrization of an infinitely divisible measure infinitely divisible as well?

answered Aug 23, 2021 at 19:55

2 votes

Accepted

Too simple proof of a unique solution of the stationary Navier-Stokes equation

answered Mar 3, 2017 at 21:24

2 votes

A characterization of trace class operators

answered May 27, 2017 at 21:12

2 votes

Accepted

Trace term in the Itō formula

answered Jun 2, 2016 at 14:16

1 vote

Accepted

Prove that $\inf_{t>0}\frac{ω(t)}t=\lim_{t\to\infty}\frac{ω(t)}t$ if $ω:[0,\infty)\toℝ$ be bounded above on every finite interval and subadditive

answered Sep 29, 2016 at 22:15

1 vote

Extension of the stochastic integral in the book "PDE and Martingale Methods in Option Pricing"

answered Oct 26, 2016 at 9:40

1 vote

If $(\mathcal D(A),A)$ is a linear operator, then $\mathcal D(A)\subseteq\mathcal D(A^{1/2})$

answered Jan 1, 2017 at 20:43

1 vote

Brownian motion, modifications vs indistinguishablity

answered Jun 15, 2017 at 16:35

1 vote

Existence of regular conditional distribution of random variable given the value of another variable

answered Nov 9, 2018 at 21:51

1 vote

Approximation of $\int_0^tF_x(s,X_s)Φ_0dW_s$ where $dX_s=φ_sds+Φ_sdW_s$ and $F_x$ is the Fréchet derivative of some $F:[0,t]×H→\mathbb R$

answered Apr 26, 2016 at 19:42

1 vote

How can we prove that the discrete Fourier transforms preserves the inner product up to a constant factor?

answered Feb 26, 2016 at 19:46

1 vote

Infinitely real-differentiable function with $f(0)=0$ but $\int_{\partial B_1(0)}\frac{f(z)}{z}dz\ne0$

answered Jun 2, 2014 at 18:09

1 vote

Accepted

A generalization of the Glivenko-Cantelli theorem

answered Nov 26, 2014 at 17:18

1 vote

Choose of the parameters related to the Wolfe-Powell conditions

answered Sep 12, 2015 at 13:49

1 vote

If $τ_x^k$ is the time of the $k$-th entrance of a Markov chain into $x$, then $\text P_x[τ_y^k<∞]=\text P_x[τ_y^1<∞](\text P_y[τ_y^1<∞])^{k-1}$

answered Oct 2, 2015 at 12:46

1 vote

If $x$ is a recurrent state of a discrete Markov chain and the probability to go from $x$ to $y$ is positive, then $y$ is recurrent

answered Oct 4, 2015 at 13:05

1 vote

Prove that the first hitting time $\tau_x:=\inf\left\{t\ge 0:B_t=x\right\}$ of a Brownian motion is almost surely finite

answered Oct 24, 2015 at 12:37

1 vote

Accepted

When are Hilbert space valued random variables independent?

answered May 9, 2017 at 16:33

1 vote

If $T$ is a positive operator then $I+T$ is invertible

answered Sep 30, 2019 at 18:31

1 vote

Accepted

Strong law of large numbers for a scaled sequence of normally distributed random variables

answered Apr 3, 2019 at 20:21

1 vote

Accepted

If $X_1,X_2$ are indep. and $Y_1,Y_2$ are indep. with $(Y_1,Y_2)∼N((x_1,x_2),σ^2I)$ if $(X_1,X_2)=(x_1,x_2)$, are $X_1(Y_1-X_1),X_2(Y_2-X_2)$ indep.?

answered Mar 28, 2019 at 9:25

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105 Answers

Sequence converging to the supremum

Measurable function applied on stationary sequence

$5$ questions on the definition of the Gelfand triple

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

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

homeomorphisms mapping interiors to interiors and boundaries to boundaries

Definition of relative (sequential) compactness

Processes $(X_t)_{t≥0}$ and $(Y_t)_{t≥0}$ are independent iff $(X_t)_{t∈I}$ and $(Y_t)_{t∈J}$ are independent for all finite $I,J⊆[0,∞)$

Abstract idea behind the method of characteristics to solve first-order PDEs

Is the symmetrization of an infinitely divisible measure infinitely divisible as well?

Too simple proof of a unique solution of the stationary Navier-Stokes equation

A characterization of trace class operators

Trace term in the Itō formula

Prove that $\inf_{t>0}\frac{ω(t)}t=\lim_{t\to\infty}\frac{ω(t)}t$ if $ω:[0,\infty)\toℝ$ be bounded above on every finite interval and subadditive

Extension of the stochastic integral in the book "PDE and Martingale Methods in Option Pricing"

If $(\mathcal D(A),A)$ is a linear operator, then $\mathcal D(A)\subseteq\mathcal D(A^{1/2})$

Brownian motion, modifications vs indistinguishablity

Existence of regular conditional distribution of random variable given the value of another variable

Approximation of $\int_0^tF_x(s,X_s)Φ_0dW_s$ where $dX_s=φ_sds+Φ_sdW_s$ and $F_x$ is the Fréchet derivative of some $F:[0,t]×H→\mathbb R$

How can we prove that the discrete Fourier transforms preserves the inner product up to a constant factor?

Infinitely real-differentiable function with $f(0)=0$ but $\int_{\partial B_1(0)}\frac{f(z)}{z}dz\ne0$

A generalization of the Glivenko-Cantelli theorem

Choose of the parameters related to the Wolfe-Powell conditions

If $τ_x^k$ is the time of the $k$-th entrance of a Markov chain into $x$, then $\text P_x[τ_y^k<∞]=\text P_x[τ_y^1<∞](\text P_y[τ_y^1<∞])^{k-1}$

If $x$ is a recurrent state of a discrete Markov chain and the probability to go from $x$ to $y$ is positive, then $y$ is recurrent

Prove that the first hitting time $\tau_x:=\inf\left\{t\ge 0:B_t=x\right\}$ of a Brownian motion is almost surely finite

When are Hilbert space valued random variables independent?

If $T$ is a positive operator then $I+T$ is invertible

Strong law of large numbers for a scaled sequence of normally distributed random variables

If $X_1,X_2$ are indep. and $Y_1,Y_2$ are indep. with $(Y_1,Y_2)∼N((x_1,x_2),σ^2I)$ if $(X_1,X_2)=(x_1,x_2)$, are $X_1(Y_1-X_1),X_2(Y_2-X_2)$ indep.?