List questions from stochastic-calculus

Published on 17 Apr 2026 - 1:24

104

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Does Itô's formula define a semimartingale?

Published on 09 Apr 2026 - 14:22

256

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Expectation of stochastic integral, martingale

Published on 29 Apr 2026 - 9:40

124

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If $Y_t=\int_0^t X_sdW_s$ where $\int_0^t X_s^2ds<\infty $ a.s., do we have that $\mathbb EY_t=0$?

Published on 16 Apr 2026 - 11:55

639

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Expectation of cubic brownian motion: $E[B_t^3]$

Published on 29 Apr 2026 - 9:40

292

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Local martingale that is not integrable

Published on 14 Apr 2026 - 14:02

136

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How to determine if the process is martingale?

Published on 11 Apr 2026 - 18:58

821

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What is the moment generating function of a function of a wiener process?

Published on 08 Apr 2026 - 16:47

269

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Independence of solution to SDE and initial condition

Published on 12 Apr 2026 - 12:29

317

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Picard's successive approximation method for SDE's

Published on 13 Apr 2026 - 19:55

38

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If $(E[\int_0^T|f_n(s)|^2ds])_n$ converges, does it exists a subsequence $f_{n(j)}$ such that the integral converges for $t<T$?

Published on 17 Apr 2026 - 12:50

24

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Equivalence Relationship for Function of Brownian Motion

Published on 29 Apr 2026 - 9:39

173

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Finding a stochastic process from Ito’s lemme on $Y_t$ such that $\int_0^1Y_s\,\mathrm{d}B_s= B_1-2B_1\mathbb{I}_{|B_1|}$

Published on 15 Apr 2026 - 23:35

101

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Time changed gaussian process

Published on 13 Apr 2026 - 23:15

615

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Fubini: Exchange of Expectation & Riemann Integration

Published on 30 Mar 2026 - 13:38

List Question

Proving $\exists C>0$ s.t. $\sup_{t\in[0,T]}\mathbb{E}(X_t^2)\leq C$ for geometric Brownian Motion

Does Itô's formula define a semimartingale?

Expectation of stochastic integral, martingale

If $Y_t=\int_0^t X_sdW_s$ where $\int_0^t X_s^2ds<\infty $ a.s., do we have that $\mathbb EY_t=0$?

Expectation of cubic brownian motion: $E[B_t^3]$

Local martingale that is not integrable

How to determine if the process is martingale?

What is the moment generating function of a function of a wiener process?

Independence of solution to SDE and initial condition

Picard's successive approximation method for SDE's

If $(E[\int_0^T|f_n(s)|^2ds])_n$ converges, does it exists a subsequence $f_{n(j)}$ such that the integral converges for $t<T$?

Equivalence Relationship for Function of Brownian Motion

Finding a stochastic process from Ito’s lemme on $Y_t$ such that $\int_0^1Y_s\,\mathrm{d}B_s= B_1-2B_1\mathbb{I}_{|B_1|}$

Time changed gaussian process

Fubini: Exchange of Expectation & Riemann Integration

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