List questions from stochastic-calculus

Published on 24 Mar 2026 - 5:48

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Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.

Published on 17 Mar 2026 - 10:49

127

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Why does there exists a random variable $x^n(t,\omega')$ such that $x_{k_r}^n$ converges to it

Published on 17 Mar 2026 - 8:02

220

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Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$

Published on 17 Mar 2026 - 7:19

35

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Mean and variance of $X:=(k-3)^2$ for $k\in\{1,\ldots,6\}$.

Published on 24 Mar 2026 - 15:54

2.4k

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4th moment of a Wiener stochastic integral?

Published on 17 Mar 2026 - 3:09

85

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Unsure how to calculate $dY_{t}$

Published on 17 Mar 2026 - 8:18

1.4k

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What techniques for proving that a stopping time is finite almost surely?

Published on 17 Mar 2026 - 16:02

319

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Optional Stopping Theorem for martingales

Published on 17 Mar 2026 - 12:02

224

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$dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$

Published on 17 Mar 2026 - 9:19

225

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Solution of an HJB equation in continuous time

Published on 20 Mar 2026 - 5:00

1.8k

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Why is $\int_0^t t \, dW_s$ not a martingale?

Published on 20 Mar 2026 - 8:59

35

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(In)dependence of solutions to certain SDEs

Published on 17 Mar 2026 - 9:53

409

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Independence of stochastic processes

Published on 22 Mar 2026 - 10:12

141

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Expectation, supremum and convergence.

Published on 17 Mar 2026 - 9:25

List Question

Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process

Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.

Why does there exists a random variable $x^n(t,\omega')$ such that $x_{k_r}^n$ converges to it

Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$

Mean and variance of $X:=(k-3)^2$ for $k\in\{1,\ldots,6\}$.

4th moment of a Wiener stochastic integral?

Unsure how to calculate $dY_{t}$

What techniques for proving that a stopping time is finite almost surely?

Optional Stopping Theorem for martingales

$dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$

Solution of an HJB equation in continuous time

Why is $\int_0^t t \, dW_s$ not a martingale?

(In)dependence of solutions to certain SDEs

Independence of stochastic processes

Expectation, supremum and convergence.

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