List questions from stochastic-calculus

Published on 29 Apr 2026 - 12:16

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Substitution of a random variable into a stochastic integral

Published on 10 May 2026 - 13:48

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Sum of two correlated geometric Brownian motions

Published on 10 May 2026 - 17:16

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Equivalence between a SDE and an ODE

Published on 10 May 2026 - 14:51

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how to Prove $τ=\inf\{t:B(t)=\max\limits_{0<s<1}B(s)\}$ is a random variable?where B(t) is brownian motion process

Published on 10 May 2026 - 12:42

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Given $dX_t = W_t^2dW_t$, and $Y_t= X_t^2$, is $Y_t$ a martingale?

Published on 10 May 2026 - 15:02

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Find $E(X_t)$ for 3 differentials $dX_t$

Published on 10 May 2026 - 16:10

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How would you find $Y_1$ for the stochastic integral $dY_t = -Y_t \hspace{1mm} dW_t + Y_t \hspace{1mm} dt$?

Published on 15 Apr 2026 - 3:52

145

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What conclusions can be made if an Ito process is differentiable?

Published on 10 May 2026 - 13:49

164

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An application of convergence of measures

Published on 10 May 2026 - 15:09

911

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Computing $\int_0^t B^n (s) \, dB(s)$ (stochastic integral)

Published on 10 May 2026 - 15:44

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How would the stochastic integral $\int_0^1 2W_t \hspace{1mm} dW_t$ be distributed?

Published on 29 Apr 2026 - 12:41

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expectation of stopped local time

Published on 10 May 2026 - 14:48

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What is the Radon-Nikodym density $dP^∗ /d P$ of the unique $P^ ∗ ∼ P$ such that the discounted price $S^*_t := S_t /B_t$ is a $P^∗$-martingale

Published on 26 Apr 2026 - 2:37

378

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Brownian Motion questions.

Published on 10 Apr 2026 - 6:20

List Question

Riemann integral of discrete white noise

Substitution of a random variable into a stochastic integral

Sum of two correlated geometric Brownian motions

Equivalence between a SDE and an ODE

how to Prove $τ=\inf\{t:B(t)=\max\limits_{0<s<1}B(s)\}$ is a random variable?where B(t) is brownian motion process

Given $dX_t = W_t^2dW_t$, and $Y_t= X_t^2$, is $Y_t$ a martingale?

Find $E(X_t)$ for 3 differentials $dX_t$

How would you find $Y_1$ for the stochastic integral $dY_t = -Y_t \hspace{1mm} dW_t + Y_t \hspace{1mm} dt$?

What conclusions can be made if an Ito process is differentiable?

An application of convergence of measures

Computing $\int_0^t B^n (s) \, dB(s)$ (stochastic integral)

How would the stochastic integral $\int_0^1 2W_t \hspace{1mm} dW_t$ be distributed?

expectation of stopped local time

What is the Radon-Nikodym density $dP^∗ /d P$ of the unique $P^ ∗ ∼ P$ such that the discounted price $S^*_t := S_t /B_t$ is a $P^∗$-martingale

Brownian Motion questions.

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