List questions from stochastic-calculus

Published on 25 Mar 2026 - 16:20

56

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If $E(|X_t-Y_t|^2)=0$, then $P\{\omega:|X_t(\omega)-Y_t(\omega)|=0,\forall t\in [0,T]\}=1$?

Published on 14 Sep 2019 - 17:20

164

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apply Ito's Lemma to X/(X+Y)

Published on 14 Sep 2019 - 22:19

611

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General stochastic integration by parts.

Published on 26 Mar 2026 - 21:07

131

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Proofs of one optional sampling theorem in Ethier & Kurtz 1986

Published on 29 Mar 2026 - 6:55

359

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Right continuity of Expectation of the Limit of a Right-Continuous Supermartingale Sequence

Published on 29 Mar 2026 - 7:00

274

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Visualize Itô differentiation rule

Published on 25 Mar 2026 - 18:24

599

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Explicit formula for product rule for Ito processes

Published on 18 Sep 2019 - 5:44

132

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Show that $ X_t = \begin{cases} W_t & \text{if $t \neq a$ } \\ 0 & \text{if $t = a$ } \end{cases} $ is not a Brownian motion

Published on 29 Mar 2026 - 0:00

726

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Calculate the stochastic integral $\int_0^T W_tdt $

Published on 26 Mar 2026 - 22:53

92

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What does the functional elements of $L^0,L^1$ and $L^\infty$ look like?

Published on 25 Mar 2026 - 23:08

48

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Covariation of Wiener processes decomposed into uncorrelated parts

Published on 26 Mar 2026 - 22:58

390

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How does one think of the "trick" in solving the GBM equation

Published on 25 Mar 2026 - 17:38

338

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Right-continuous and Progressively measurability of Lebesgue-Stieltjes integrals

Published on 26 Mar 2026 - 22:53

19

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Let $X_t=\int_0^t f(X_s)ds+W_t$ where $f$ is continuous. Why $X\in W^{1,2}$?

Published on 26 Sep 2019 - 10:10

List Question

mean and variance of the SDE $dy_{t}=\nu(\mu-y_{t})dt+J_{t}dN_{t}\sigma dW_{t}$

If $E(|X_t-Y_t|^2)=0$, then $P\{\omega:|X_t(\omega)-Y_t(\omega)|=0,\forall t\in [0,T]\}=1$?

apply Ito's Lemma to X/(X+Y)

General stochastic integration by parts.

Proofs of one optional sampling theorem in Ethier & Kurtz 1986

Right continuity of Expectation of the Limit of a Right-Continuous Supermartingale Sequence

Visualize Itô differentiation rule

Explicit formula for product rule for Ito processes

Show that $ X_t = \begin{cases} W_t & \text{if $t \neq a$ } \\ 0 & \text{if $t = a$ } \end{cases} $ is not a Brownian motion

Calculate the stochastic integral $\int_0^T W_tdt $

What does the functional elements of $L^0,L^1$ and $L^\infty$ look like?

Covariation of Wiener processes decomposed into uncorrelated parts

How does one think of the "trick" in solving the GBM equation

Right-continuous and Progressively measurability of Lebesgue-Stieltjes integrals

Let $X_t=\int_0^t f(X_s)ds+W_t$ where $f$ is continuous. Why $X\in W^{1,2}$?

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