List questions from stopping-times

89

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First passage time $T_{B}^{'}=\inf\{t\geq0:X_{t}\in B\}$ is stopping time when $B$ is open or closed set

Published on 17 Mar 2026 - 14:13

344

Views

Why the Brownian motion stopped at the local time is a martingale?

Published on 19 Mar 2026 - 22:06

53

Views

Stopping time of dependent gaussians variables

Published on 24 Apr 2018 - 9:32

46

Views

Can this be viewed as a random walk?

Published on 24 Apr 2018 - 18:24

926

Views

Hitting time of Brownian motion against a square root curve

Published on 24 Apr 2018 - 18:24

174

Views

(Advanced) Strong Markov Property

Published on 26 Apr 2018 - 10:05

197

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$\sum \xi_n<\infty \;\text{a.e.}\; \rightarrow \sum \sigma_n^2 < \infty$ if $E(\xi_n)=0$ and $V(\xi_n)=\sigma_n^2<\infty$.

Published on 26 Apr 2018 - 19:43

51

Views

What if $X_k(\omega)$ isn't uniformly bounded for $\omega$?

Published on 27 Apr 2018 - 13:57

629

Views

Derive PDE from $n^{\text{th}}$ moment of stopping time of SDE

Published on 30 Apr 2018 - 8:21

278

Views

simple random walk and stopping time

Published on 02 May 2018 - 21:54

239

Views

Compute $P(T< \infty)$

Published on 03 May 2018 - 7:02

65

Views

Are $\xi_n(s)=1_{\{s\le\tau_n\wedge t\}}$ elementary processes ?

Published on 07 May 2018 - 15:39

47

Views

Simple inequality for a stopped process depending Hölder continuously on a spatial parameter

Published on 13 May 2018 - 20:54

354

Views

Hitting time defined by another hitting time is a stopping time.

Published on 16 May 2018 - 3:30

63

Views

Boundedness of a stochastic process and martingale convergence

Published on 17 May 2018 - 9:10

List Question

First passage time $T_{B}^{'}=\inf\{t\geq0:X_{t}\in B\}$ is stopping time when $B$ is open or closed set

Why the Brownian motion stopped at the local time is a martingale?

Stopping time of dependent gaussians variables

Can this be viewed as a random walk?

Hitting time of Brownian motion against a square root curve

(Advanced) Strong Markov Property

$\sum \xi_n<\infty \;\text{a.e.}\; \rightarrow \sum \sigma_n^2 < \infty$ if $E(\xi_n)=0$ and $V(\xi_n)=\sigma_n^2<\infty$.

What if $X_k(\omega)$ isn't uniformly bounded for $\omega$?

Derive PDE from $n^{\text{th}}$ moment of stopping time of SDE

simple random walk and stopping time

Compute $P(T< \infty)$

Are $\xi_n(s)=1_{\{s\le\tau_n\wedge t\}}$ elementary processes ?

Simple inequality for a stopped process depending Hölder continuously on a spatial parameter

Hitting time defined by another hitting time is a stopping time.

Boundedness of a stochastic process and martingale convergence

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