List questions from stochastic-analysis

Published on 14 Feb 2020 - 18:13

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Whether two one-dimensional Brownian motions yield a two-dimensional Brownian motion

Published on 15 Feb 2020 - 7:47

218

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Why is a Polish space a standard measurable space?

Published on 23 Feb 2026 - 4:53

346

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Calculating a quadratic variation of a process

Published on 28 Mar 2026 - 5:28

502

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The equivalence between almost surely continuous and continuous modification

Published on 16 Feb 2020 - 19:46

475

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Show that $(X_{t})_{t\in[0,1]}$ of i.i.d random variables with non-degenerate distribution has no continuous modification

Published on 17 Feb 2020 - 1:03

429

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Understanding the $L^{2}-$Limit of Gaussian Random Vectors

Published on 18 Feb 2020 - 16:44

231

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Show that $\mathbb{E}(X_{0}|X_{1},\cdots,X_{n})=c_{0}+c_{1}X_{1}+\cdots+c_{n}X_{n}$ for $(X_{0},\cdots, X_{n})$ Guassian.

Published on 19 Feb 2020 - 3:28

342

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An easier way to check the existence of continuous modification without using Chentsov-Kolmogorov Theorem.

Published on 19 Feb 2020 - 21:23

123

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Show that for any centered Gaussian process $X$, there exists a non-decreasing function $f$ and a Wiener process $W$ such that $X(t)=W(f(t))$ is true.

Published on 21 Feb 2020 - 2:53

419

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Why $X_t:=\sqrt t B_1$ and $Y_t:=B_{2t}-B_t$ are not a Brownian motion?

Published on 21 Feb 2020 - 11:32

103

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Variance of a second order stochastic differential equation

Published on 28 Mar 2026 - 8:45

257

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Convergence of an Ornstein-Uhlenbeck Process

Published on 26 Mar 2026 - 6:05

186

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Decomposition of Two related Brownian Motion

Published on 25 Feb 2020 - 14:55

183

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Simple Stochastic Calculus Cauchy Schwarz

Published on 28 Mar 2026 - 8:47

List Question

Compute the characteristic function of Wiener Process (Brownian Motion).

Whether two one-dimensional Brownian motions yield a two-dimensional Brownian motion

Why is a Polish space a standard measurable space?

Calculating a quadratic variation of a process

The equivalence between almost surely continuous and continuous modification

Show that $(X_{t})_{t\in[0,1]}$ of i.i.d random variables with non-degenerate distribution has no continuous modification

Understanding the $L^{2}-$Limit of Gaussian Random Vectors

Show that $\mathbb{E}(X_{0}|X_{1},\cdots,X_{n})=c_{0}+c_{1}X_{1}+\cdots+c_{n}X_{n}$ for $(X_{0},\cdots, X_{n})$ Guassian.

An easier way to check the existence of continuous modification without using Chentsov-Kolmogorov Theorem.

Show that for any centered Gaussian process $X$, there exists a non-decreasing function $f$ and a Wiener process $W$ such that $X(t)=W(f(t))$ is true.

Why $X_t:=\sqrt t B_1$ and $Y_t:=B_{2t}-B_t$ are not a Brownian motion?

Variance of a second order stochastic differential equation

Convergence of an Ornstein-Uhlenbeck Process

Decomposition of Two related Brownian Motion

Simple Stochastic Calculus Cauchy Schwarz

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