List questions from stochastic-analysis

Published on 22 Mar 2026 - 13:11

47

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under what conditions stochastic exponential is a usual exponential?

Published on 23 Apr 2018 - 0:35

31

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Formula Product of Random Variables

Published on 23 Apr 2018 - 21:53

142

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Please ignore the scary length of the proof! I only query two lines! (Brownian Motion Notation/ Doob's Theorem)

Published on 22 Mar 2026 - 2:24

111

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Why do we need absolute continuity of the mapping $t \mapsto \langle M \rangle_t(\omega)$ wr.t to the Lebesgue measure for almost all $\omega$?

Published on 25 Mar 2026 - 4:43

578

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When is the quadratic variation of a process continuously differentiable?

Published on 25 Mar 2026 - 6:01

82

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Convergence in $L^2$ of non-atomic Gaussian measure on Polish space.

Published on 08 May 2018 - 20:58

56

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Type of convergence for random variables

Published on 08 May 2018 - 22:21

559

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Let $B = \{B_t : t \geq 0\}$ be a pre-Brownian motion. Show that $B^a$ is independent of $\sigma(B_r : r \leq a)$ for every $a \geq 0$.

Published on 25 Mar 2026 - 12:50

130

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A question about pinned Gaussian processes

Published on 09 May 2018 - 17:08

96

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Does the Levy process stay in any open ball at any fixed time with positive probability?

Published on 10 May 2018 - 3:11

283

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Is there a relation between derivative of a smooth path and the signature?

Published on 25 Mar 2026 - 9:27

1.3k

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Find $P(B(s)>0, B(t)>0)$, where $B(s)$ is Brownian motion, $s<t$.

Published on 25 Mar 2026 - 14:26

613

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Find $E(B_{1}^2B_{2}B_{3})$, where $B_{i}$ is Brownian motion

Published on 25 Mar 2026 - 12:52

234

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Extreme points of a subset of density functions

Published on 25 Mar 2026 - 6:05

List Question

Proof of Non-differentiability of Brownian motion using local times

under what conditions stochastic exponential is a usual exponential?

Formula Product of Random Variables

Please ignore the scary length of the proof! I only query two lines! (Brownian Motion Notation/ Doob's Theorem)

Why do we need absolute continuity of the mapping $t \mapsto \langle M \rangle_t(\omega)$ wr.t to the Lebesgue measure for almost all $\omega$?

When is the quadratic variation of a process continuously differentiable?

Convergence in $L^2$ of non-atomic Gaussian measure on Polish space.

Type of convergence for random variables

Let $B = \{B_t : t \geq 0\}$ be a pre-Brownian motion. Show that $B^a$ is independent of $\sigma(B_r : r \leq a)$ for every $a \geq 0$.

A question about pinned Gaussian processes

Does the Levy process stay in any open ball at any fixed time with positive probability?

Is there a relation between derivative of a smooth path and the signature?

Find $P(B(s)>0, B(t)>0)$, where $B(s)$ is Brownian motion, $s<t$.

Find $E(B_{1}^2B_{2}B_{3})$, where $B_{i}$ is Brownian motion

Extreme points of a subset of density functions

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