List questions from brownian-motion

221

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Let $\{B_t\}_{t \ge 0}$ a Brownian Motion, prove that for all $a \gt 0$: $P(B_t \ge a$ for some $t \ge 0 )=1$

Published on 25 May 2019 - 0:16

587

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Gaussian process is a Brownian motion.

Published on 25 May 2019 - 12:58

79

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Lévy processes, Brownian motion and Lie groups

Published on 26 Mar 2026 - 1:07

49

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$\xi$ has modification $\eta$ with continuous paths $\iff \exists c \in \mathbb R$ s.t. $P(\xi_{0}=c)=1$

Published on 26 May 2019 - 23:00

237

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Ito integral related proofs

Published on 28 May 2019 - 17:08

190

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Is an integrated Wiener process recurrent or transient?

Published on 26 Mar 2026 - 14:18

198

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Version of Tanaka's Formula outside Brownian Motion

Published on 31 May 2019 - 4:01

109

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Supremum of Brownian motion almost surely not at endpoint

Published on 02 Jun 2019 - 12:59

415

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Brownian Motion and Complex Analysis

Published on 03 Jun 2019 - 8:46

60

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HJB when optimal control responds partially to Brownian motion

Published on 25 Mar 2026 - 6:11

29

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Is isotopy type of brownian loops deterministic?

Published on 25 Mar 2026 - 17:52

1.3k

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Proof of Blumenthal's 0-1 law for Brownian Motion

Published on 03 Jun 2019 - 15:54

649

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Revuz and Yor's Book “Continuous Martingales and Brownian Motion” - Chapter 1 - Exercise 1.19

Published on 03 Jun 2019 - 16:03

858

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Quadratic variation of $w^2(t)$

Published on 27 Mar 2026 - 2:22

701

Views

Hitting times by Brownian motion

Published on 25 Mar 2026 - 20:34

List Question

Let $\{B_t\}_{t \ge 0}$ a Brownian Motion, prove that for all $a \gt 0$: $P(B_t \ge a$ for some $t \ge 0 )=1$

Gaussian process is a Brownian motion.

Lévy processes, Brownian motion and Lie groups

$\xi$ has modification $\eta$ with continuous paths $\iff \exists c \in \mathbb R$ s.t. $P(\xi_{0}=c)=1$

Ito integral related proofs

Is an integrated Wiener process recurrent or transient?

Version of Tanaka's Formula outside Brownian Motion

Supremum of Brownian motion almost surely not at endpoint

Brownian Motion and Complex Analysis

HJB when optimal control responds partially to Brownian motion

Is isotopy type of brownian loops deterministic?

Proof of Blumenthal's 0-1 law for Brownian Motion

Revuz and Yor's Book “Continuous Martingales and Brownian Motion” - Chapter 1 - Exercise 1.19

Quadratic variation of $w^2(t)$

Hitting times by Brownian motion

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