List questions from stochastic-calculus

Published on 16 Apr 2026 - 1:46

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Compute integral with correlated brownian motions

Published on 29 Apr 2026 - 10:30

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Question on $\mathbb E_{X_{t_{n-2}}}[1_{B_{n-1}}(X_{t_{n-1}-t_{n-2}})\mathbb E_{X_{t_{n-1}}}[1_{B_{n}}(X_{t_{n}-t_{n-1}})]]$

Published on 17 Apr 2026 - 2:50

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How to solve $dY_t = dt + 2 \sqrt{Y_t} dW_t$?

Published on 16 Apr 2026 - 2:20

157

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How to differentiate this exponential process?

Published on 09 Apr 2026 - 3:29

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$L^2$decomposition

Published on 28 Apr 2026 - 0:34

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Let $B = (B_t)_{t \geq 0}$ be a standard brownian motion and $I_t = \inf_{0 \leq s \leq t} B_s$, show $F(t, B_t, I_t)$ is a martingale.

Published on 16 Apr 2026 - 0:53

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How can a discrete stochastic integral be used to show that $(X_n)$ submartingale, $S\le T\implies E(X_S)\le E(X_T)$

Published on 14 Apr 2026 - 7:00

493

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moments of a Geometric brownian motion using Ito's lemma

Published on 09 Apr 2026 - 1:57

380

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Dynkin Operator explained to a finance student

Published on 09 Apr 2026 - 20:33

130

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Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

Published on 14 Apr 2026 - 13:32

338

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Regarding sample continuity of Gaussian Processes

Published on 14 Apr 2026 - 9:43

88

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Show that $Z_t = \sqrt{\sqrt{2t}e^{-\sqrt{2t}}} B_{e^{\sqrt{2t}}-1}$ solves $dZ_t = f(t)Z_tdt +dM_t$ and find $f(t)$.

Published on 16 Apr 2026 - 19:10

344

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Compute $E(2B_T e^{-B_T}+ 4e^{-B_T})$ for $B = (B_t)_{t \geq 0}$ a standard Brownian motion and $T=\inf\{t \geq 0 : |B_t|=1\}$.

Published on 16 Apr 2026 - 4:47

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Using Novikov Theorem to Derive Fokker-Planck/ Smoluchowksi Equation

Published on 29 Apr 2026 - 11:30

List Question

$M = (M_t)_{t\geq 0}$ obtained by Itô's formula is a martingale

Compute integral with correlated brownian motions

Question on $\mathbb E_{X_{t_{n-2}}}[1_{B_{n-1}}(X_{t_{n-1}-t_{n-2}})\mathbb E_{X_{t_{n-1}}}[1_{B_{n}}(X_{t_{n}-t_{n-1}})]]$

How to solve $dY_t = dt + 2 \sqrt{Y_t} dW_t$?

How to differentiate this exponential process?

$L^2$decomposition

Let $B = (B_t)_{t \geq 0}$ be a standard brownian motion and $I_t = \inf_{0 \leq s \leq t} B_s$, show $F(t, B_t, I_t)$ is a martingale.

How can a discrete stochastic integral be used to show that $(X_n)$ submartingale, $S\le T\implies E(X_S)\le E(X_T)$

moments of a Geometric brownian motion using Ito's lemma

Dynkin Operator explained to a finance student

Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

Regarding sample continuity of Gaussian Processes

Show that $Z_t = \sqrt{\sqrt{2t}e^{-\sqrt{2t}}} B_{e^{\sqrt{2t}}-1}$ solves $dZ_t = f(t)Z_tdt +dM_t$ and find $f(t)$.

Compute $E(2B_T e^{-B_T}+ 4e^{-B_T})$ for $B = (B_t)_{t \geq 0}$ a standard Brownian motion and $T=\inf\{t \geq 0 : |B_t|=1\}$.

Using Novikov Theorem to Derive Fokker-Planck/ Smoluchowksi Equation

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