List questions from stochastic-calculus

Published on 18 Feb 2020 - 21:55

232

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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 28 Mar 2026 - 15:36

343

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

Published on 28 Mar 2026 - 15:35

124

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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 28 Mar 2026 - 15:36

345

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Find the analytical solution of a stochastic integral equation

Published on 21 Feb 2020 - 10:57

103

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Variance of a second order stochastic differential equation

Published on 28 Mar 2026 - 8:45

1.2k

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Application of the Girsanov theorem

Published on 21 Feb 2020 - 20:09

79

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Characteristic function of Multi dimensional Brownian motion stopped at hitting time

Published on 23 Feb 2020 - 7:27

70

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Relating two equations in a jump-diffusion process

Published on 26 Mar 2026 - 6:02

187

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Decomposition of Two related Brownian Motion

Published on 28 Mar 2026 - 15:35

115

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Effective Drift Due to Conditional Stochastic Process.

Published on 27 Mar 2026 - 8:46

205

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Weak solution to Stochastic differential equations

Published on 26 Mar 2026 - 7:40

183

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Simple Stochastic Calculus Cauchy Schwarz

Published on 28 Mar 2026 - 8:47

1.4k

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Searching for a second order ODE whose solution is bell shape (Gaussian function)

Published on 23 Feb 2026 - 2:34

33

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What is wrong, or what is missing from the following statement?

Published on 23 Feb 2026 - 6:18

List Question

$W(s)[W(t)-W(s)]$ Independence for Brownian Motion

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.

Find the analytical solution of a stochastic integral equation

Variance of a second order stochastic differential equation

Application of the Girsanov theorem

Characteristic function of Multi dimensional Brownian motion stopped at hitting time

Relating two equations in a jump-diffusion process

Decomposition of Two related Brownian Motion

Effective Drift Due to Conditional Stochastic Process.

Weak solution to Stochastic differential equations

Simple Stochastic Calculus Cauchy Schwarz

Searching for a second order ODE whose solution is bell shape (Gaussian function)

What is wrong, or what is missing from the following statement?

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