List questions from stochastic-calculus

Published on 09 Apr 2026 - 22:17

69

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Write stochastic integral equation in differential form.

Published on 13 Apr 2026 - 20:37

294

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Linearization of a SDE and comparison to deterministic setting

Published on 13 Apr 2026 - 19:33

89

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Scaling of white noise from scaling of brownian motion

Published on 10 Apr 2026 - 1:07

177

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Stopping time w.r.t Brownian filtration is predictable

Published on 15 Apr 2026 - 3:15

91

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Connection between semimartingales in Itô calculus and measures in integration theory

Published on 08 Apr 2026 - 19:18

31

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Expected Discount Factor with respect to First Passage Time

Published on 10 Apr 2026 - 23:08

127

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Let $\alpha > 0$, $M_t=\exp(\alpha B_t - \alpha^2 t/2)$ for all $t \ge 0$. Show that $M_t \to 0$ a.s.

Published on 17 Apr 2026 - 15:45

40

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Simplifying terms in Ito's Lemma like $Y_t dX_t$ and $dX_tdY_t$

Published on 13 Apr 2026 - 17:56

93

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Missing Step Showing That $M_t = \exp(\alpha B_t - \alpha^2 t/2)$ doesn't converge to $0$ in $L^1$ norm.

Published on 16 Apr 2026 - 12:43

123

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maximum of the increment of brownian motion when partition norm tends to 0

Published on 29 Apr 2026 - 13:28

367

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Strong law of large numbers - Continuous martingales - Reference request

Published on 13 Apr 2026 - 7:48

122

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Quadratic variation - Solution check

Published on 12 Apr 2026 - 12:36

139

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Prove that $\sup_{0\leq s\leq t}\mathbb E[|X_s|^2]<\infty $ where $dX_s=\mu(X_s,s)ds+\sigma (X_s,s)dW_s$

Published on 15 Apr 2026 - 18:08

135

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Concentration for stochastic integral involving the Brownian motion itself

Published on 09 Apr 2026 - 19:47

List Question

Itô's formula for an expectation result

Write stochastic integral equation in differential form.

Linearization of a SDE and comparison to deterministic setting

Scaling of white noise from scaling of brownian motion

Stopping time w.r.t Brownian filtration is predictable

Connection between semimartingales in Itô calculus and measures in integration theory

Expected Discount Factor with respect to First Passage Time

Let $\alpha > 0$, $M_t=\exp(\alpha B_t - \alpha^2 t/2)$ for all $t \ge 0$. Show that $M_t \to 0$ a.s.

Simplifying terms in Ito's Lemma like $Y_t dX_t$ and $dX_tdY_t$

Missing Step Showing That $M_t = \exp(\alpha B_t - \alpha^2 t/2)$ doesn't converge to $0$ in $L^1$ norm.

maximum of the increment of brownian motion when partition norm tends to 0

Strong law of large numbers - Continuous martingales - Reference request

Quadratic variation - Solution check

Prove that $\sup_{0\leq s\leq t}\mathbb E[|X_s|^2]<\infty $ where $dX_s=\mu(X_s,s)ds+\sigma (X_s,s)dW_s$

Concentration for stochastic integral involving the Brownian motion itself

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