List questions from stochastic-calculus

Published on 11 Apr 2026 - 16:32

52

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Why $\int_t^T \int_0^s f(s,u)dW(u)ds=\int_0^t \int_t^T f(s,u)dsdW(u)+\int_t^T \int_u^Tf(s,u)dsdW(u)$??

Published on 17 Apr 2026 - 8:34

127

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Brownian local time: can we estimate $\mathbb{E}^B\left[\int_{\mathbb{R}}\left|L_{a}(t)-L_{a}(s)\right|^2da\right]$?

Published on 15 Apr 2026 - 4:02

232

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Expectation of Brownian motion at a stopping time depending on a brownian motion

Published on 13 Apr 2026 - 6:27

77

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How to use Stochastic integration by parts

Published on 11 Apr 2026 - 20:16

76

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Making an ansatz for solving a SDE

Published on 11 Apr 2026 - 19:40

378

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Showing that $\sup\{t\leq1:W_t=1\}$ is not a stopping time

Published on 30 Apr 2026 - 9:41

36

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Integrating factor for guessing starting solution for SDE

Published on 12 Apr 2026 - 14:18

32

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Time-Dependent Moments of General SDEs

Published on 16 Apr 2026 - 5:37

134

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How do you find the expectation of a random variable involving a function of Brownian motions?

Published on 30 Apr 2026 - 9:41

62

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Squared distance to a closed embedded manifold

Published on 14 Apr 2026 - 0:01

32

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Why can we split product averages of stochastic processes? $\langle x(t_1)x(t_2)\dots x(t_N) \rangle = \langle x(t_1)x(t_2)\rangle \dots$

Published on 17 Apr 2026 - 11:24

128

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How do you find the expectation of process involving Brownian motions at different times?

Published on 30 Apr 2026 - 9:41

26

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Expected value of first duplication by sampling elements with replacement

Published on 10 Apr 2026 - 16:19

34

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Is this calculation of the expectation of Brownian motion correct?

Published on 30 Apr 2026 - 9:41

List Question

Solution for $dX=dt+2\sqrt{X}dW$ with positive-valued $\sqrt{X}$

Why $\int_t^T \int_0^s f(s,u)dW(u)ds=\int_0^t \int_t^T f(s,u)dsdW(u)+\int_t^T \int_u^Tf(s,u)dsdW(u)$??

Brownian local time: can we estimate $\mathbb{E}^B\left[\int_{\mathbb{R}}\left|L_{a}(t)-L_{a}(s)\right|^2da\right]$?

Expectation of Brownian motion at a stopping time depending on a brownian motion

How to use Stochastic integration by parts

Making an ansatz for solving a SDE

Showing that $\sup\{t\leq1:W_t=1\}$ is not a stopping time

Integrating factor for guessing starting solution for SDE

Time-Dependent Moments of General SDEs

How do you find the expectation of a random variable involving a function of Brownian motions?

Squared distance to a closed embedded manifold

Why can we split product averages of stochastic processes? $\langle x(t_1)x(t_2)\dots x(t_N) \rangle = \langle x(t_1)x(t_2)\rangle \dots$

How do you find the expectation of process involving Brownian motions at different times?

Expected value of first duplication by sampling elements with replacement

Is this calculation of the expectation of Brownian motion correct?

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