List questions from stochastic-calculus

Published on 12 Apr 2026 - 14:57

138

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Finding Expectation of a Stochastic Differential Equation Solution

Published on 04 May 2026 - 22:38

96

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Wald lemma and Brownian motion

Published on 04 May 2026 - 22:38

115

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How do I prove that $\Bbb{P}(|X_n|>n~~i.o.)=0$?

Published on 14 Apr 2026 - 15:04

53

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Show that $f(t, B_t)$ is only a function about $t$.

Published on 14 Apr 2026 - 15:04

142

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Showing that a diffusion process is positive recurrent

Published on 12 Apr 2026 - 13:38

454

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Itô integral with brownian motion powers

Published on 04 May 2026 - 23:40

291

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Parameter Estimation of Stochastic Process

Published on 09 Apr 2026 - 5:24

65

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Conditioning by a random function

Published on 06 May 2026 - 6:51

214

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Proof verification: conditional distribution of integral of brownian motion

Published on 12 Apr 2026 - 17:43

59

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Suppose the quadratic covariation of process $X$ with $B$ is constant - then is $X$ linear in $B$?

Published on 14 Apr 2026 - 11:49

64

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Show that the solution is given by $Y_t=\mathcal{E}(X)_t(H_0+\int_0^t\mathcal{E}(X)_s^{-1}(dH_s-d[H,X]_s)) $.

Published on 15 Apr 2026 - 9:08

372

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Expectation of modified Ornstein-Uhlenbeck process with random long run mean

Published on 10 Apr 2026 - 17:50

88

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What is $ d B_t \sqrt{d t} $, where $B_t$ is the Brownian motion on $\mathbb{R}$?

Published on 15 Apr 2026 - 6:56

35

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$\mathbb{E}[(\int_{0}^{t} V_s^2: d\langle M^{c}\rangle_{s})^{\frac{1}{2}}]<\infty$ implies $N_t:= \int_0^t V_s \cdot d M_{s}^{c}$ is a martingale.

Published on 16 Apr 2026 - 19:47

List Question

Definitions of the Stratonovich integral and why the "average" definition is arguably correct

Finding Expectation of a Stochastic Differential Equation Solution

Wald lemma and Brownian motion

How do I prove that $\Bbb{P}(|X_n|>n~~i.o.)=0$?

Show that $f(t, B_t)$ is only a function about $t$.

Showing that a diffusion process is positive recurrent

Itô integral with brownian motion powers

Parameter Estimation of Stochastic Process

Conditioning by a random function

Proof verification: conditional distribution of integral of brownian motion

Suppose the quadratic covariation of process $X$ with $B$ is constant - then is $X$ linear in $B$?

Show that the solution is given by $Y_t=\mathcal{E}(X)_t(H_0+\int_0^t\mathcal{E}(X)_s^{-1}(dH_s-d[H,X]_s)) $.

Expectation of modified Ornstein-Uhlenbeck process with random long run mean

What is $ d B_t \sqrt{d t} $, where $B_t$ is the Brownian motion on $\mathbb{R}$?

$\mathbb{E}[(\int_{0}^{t} V_s^2: d\langle M^{c}\rangle_{s})^{\frac{1}{2}}]<\infty$ implies $N_t:= \int_0^t V_s \cdot d M_{s}^{c}$ is a martingale.

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