List questions from brownian-motion

Published on 07 Dec 2018 - 3:03

503

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Brownian motion : what is it exactly and why is it so important?

Published on 25 Mar 2026 - 1:41

2.5k

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Probability on first hitting time of Brownian motion with drift

Published on 25 Mar 2026 - 11:20

107

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Why is $T:=\inf\{t\geq0:B_t\leq at^p-b\}$ a stopping time?

Published on 25 Mar 2026 - 11:21

34

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Why is $P^b(B_{T-T_b} \in (-\infty,b))=1/2$

Published on 26 Mar 2026 - 9:40

511

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Proving Kolmogorov's continuity condition holds for Brownian motion?

Published on 11 Dec 2018 - 4:44

41

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Proving alternative notation of quadratic variation of Brownian motion

Published on 11 Dec 2018 - 7:25

140

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Show that this processes are martingales

Published on 12 Dec 2018 - 9:24

218

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Show $(B_t )^2$ i.e. square of a Brownian motion is a Markov process.

Published on 26 Mar 2026 - 11:17

72

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Is the following stopping time finite: $T:=\inf\{t\geq 0:B_t\geq \sqrt{t}+1\}?$

Published on 25 Mar 2026 - 11:21

69

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Differential of Stochastic process

Published on 25 Mar 2026 - 23:36

1.1k

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What's the distribution of $\int tW(t)dt$ for Brownian motion $W(t)$

Published on 14 Dec 2018 - 1:25

97

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Hitting time distribution with exponential growth

Published on 25 Mar 2026 - 11:17

711

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If $\tau=\inf \{t \ge 0: B(t)= -a \text{ or } b\}$ is a stopping time of Brownian motion $B_t$, why does $E(\tau)=E(B_{\tau}^2)$?

Published on 25 Mar 2026 - 12:49

315

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Show that stochastic integral w.r.t. Brownian motion is normal distributed

Published on 25 Mar 2026 - 23:36

List Question

Brownian motion reflection principle result

Brownian motion : what is it exactly and why is it so important?

Probability on first hitting time of Brownian motion with drift

Why is $T:=\inf\{t\geq0:B_t\leq at^p-b\}$ a stopping time?

Why is $P^b(B_{T-T_b} \in (-\infty,b))=1/2$

Proving Kolmogorov's continuity condition holds for Brownian motion?

Proving alternative notation of quadratic variation of Brownian motion

Show that this processes are martingales

Show $(B_t )^2$ i.e. square of a Brownian motion is a Markov process.

Is the following stopping time finite: $T:=\inf\{t\geq 0:B_t\geq \sqrt{t}+1\}?$

Differential of Stochastic process

What's the distribution of $\int tW(t)dt$ for Brownian motion $W(t)$

Hitting time distribution with exponential growth

If $\tau=\inf \{t \ge 0: B(t)= -a \text{ or } b\}$ is a stopping time of Brownian motion $B_t$, why does $E(\tau)=E(B_{\tau}^2)$?

Show that stochastic integral w.r.t. Brownian motion is normal distributed

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