List questions from brownian-motion

96

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Question about Rene Schilling's construction of Brownian Motion using complete ONS: Taking a $L^2$ limit out of the exponential

Published on 22 Apr 2020 - 8:02

612

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Joint distribution of hitting times for brownian motion with drift

Published on 29 Mar 2026 - 20:38

186

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SDE for Brownian motion on $S^n$

Published on 26 Mar 2026 - 10:46

424

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Non-differentiability of the Brownian motion

Published on 26 Mar 2026 - 10:46

629

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Integrated brownian motion is not a Markov process

Published on 29 Mar 2026 - 14:00

128

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$_(,_)$ is a martingale

Published on 30 Mar 2026 - 0:17

533

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Infinitesimal generator - Feller semigroup

Published on 02 Apr 2026 - 14:38

28

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Computing $E_x[\mathrm e^{-\theta^2(\tau-\sigma)/2}]$ when $\tau$ and $\sigma$ are first exit times of an interval.

Published on 26 Apr 2020 - 21:19

172

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Brownian motion : first time it reach $1$ is in mean infinite. Does it make sense?

Published on 27 Apr 2020 - 8:51

37

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Why squaring the LHS result in the RHS having a sigma term??

Published on 29 Mar 2026 - 16:34

200

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Solve the Stochastic Differential Equation (Ito's Formula)

Published on 26 Mar 2026 - 12:13

60

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Evaluate stochastic integration

Published on 29 Mar 2026 - 10:26

911

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Use the martingale $M_t = \exp(\theta B_t − \theta^2t/2)$, $\theta \in \mathbb{R}$, to find $P(\tau_a < \tau_b)$

Published on 27 Mar 2026 - 14:52

41

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Augmentation of the process with left-continuous paths

Published on 02 Apr 2026 - 16:30

80

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Brownian mottion and hitting probabilities

Published on 28 Mar 2026 - 6:58

List Question

Question about Rene Schilling's construction of Brownian Motion using complete ONS: Taking a $L^2$ limit out of the exponential

Joint distribution of hitting times for brownian motion with drift

SDE for Brownian motion on $S^n$

Non-differentiability of the Brownian motion

Integrated brownian motion is not a Markov process

$_(,_)$ is a martingale

Infinitesimal generator - Feller semigroup

Computing $E_x[\mathrm e^{-\theta^2(\tau-\sigma)/2}]$ when $\tau$ and $\sigma$ are first exit times of an interval.

Brownian motion : first time it reach $1$ is in mean infinite. Does it make sense?

Why squaring the LHS result in the RHS having a sigma term??

Solve the Stochastic Differential Equation (Ito's Formula)

Evaluate stochastic integration

Use the martingale $M_t = \exp(\theta B_t − \theta^2t/2)$, $\theta \in \mathbb{R}$, to find $P(\tau_a < \tau_b)$

Augmentation of the process with left-continuous paths

Brownian mottion and hitting probabilities

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