List questions from stochastic-calculus

Published on 12 Apr 2026 - 7:44

25

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Doob-Meyer decomposition of number of times the diffusion cross a barrier

Published on 15 Apr 2026 - 14:30

86

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Expectation of the exponential of the sum of Brownian motion and the time it spent above certain threshold

Published on 14 Apr 2026 - 2:19

56

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Can we show that for any $s > t ≥ 0$, we have $\mathbb{E}[\omega_s|\omega_t] =e^{\kappa(s−t)}\omega_t$ and why?

Published on 15 Apr 2026 - 19:03

46

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Can stochastic PDE theory be applied to elliptic PDE to get the solvability when it's hard to use traditional prior estimate or flow approach

Published on 11 Apr 2026 - 14:17

57

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Why do I have $\Bbb{E}\left(|\Bbb{E}(X|Y)|\right)=\sum_{y\in E'} \Bbb{E}\left(|\Bbb{E}(X|Y)|\Bbb{1}_{Y=y}\right)$?

Published on 14 Apr 2026 - 5:47

47

Views

Problem with weak law of large numbers

Published on 11 Apr 2026 - 15:13

73

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Variance of Itô integral

Published on 14 Apr 2026 - 4:00

132

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Scaling properties of Hölder seminorms

Published on 10 Apr 2026 - 21:41

204

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How can I show that $\Bbb{E}(f(X)g(Y)|X)=f(X)\Bbb{E}(g(Y))$?

Published on 16 Apr 2026 - 8:06

191

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Stochastic process with Student's t-distribution

Published on 09 Apr 2026 - 16:47

84

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Computing the expected quadratic variation of a Brownian bridge

Published on 09 Apr 2026 - 18:23

62

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Expected value of exponential integrate Brownian motion

Published on 10 Apr 2026 - 17:50

101

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Why is it possible to substitute in differential form?

Published on 12 Apr 2026 - 14:30

67

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Conditional expectation of the exponential of the integral of a diffusion

Published on 14 Apr 2026 - 17:21

List Question

Probability problem with 3 dice

Doob-Meyer decomposition of number of times the diffusion cross a barrier

Expectation of the exponential of the sum of Brownian motion and the time it spent above certain threshold

Can we show that for any $s > t ≥ 0$, we have $\mathbb{E}[\omega_s|\omega_t] =e^{\kappa(s−t)}\omega_t$ and why?

Can stochastic PDE theory be applied to elliptic PDE to get the solvability when it's hard to use traditional prior estimate or flow approach

Why do I have $\Bbb{E}\left(|\Bbb{E}(X|Y)|\right)=\sum_{y\in E'} \Bbb{E}\left(|\Bbb{E}(X|Y)|\Bbb{1}_{Y=y}\right)$?

Problem with weak law of large numbers

Variance of Itô integral

Scaling properties of Hölder seminorms

How can I show that $\Bbb{E}(f(X)g(Y)|X)=f(X)\Bbb{E}(g(Y))$?

Stochastic process with Student's t-distribution

Computing the expected quadratic variation of a Brownian bridge

Expected value of exponential integrate Brownian motion

Why is it possible to substitute in differential form?

Conditional expectation of the exponential of the integral of a diffusion

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