Question

Iterated optional times

score 32 · Answer 1 · 2021-10-05 22:55:58

32

Views

Iterated optional times

Published on 05 Oct 2021 - 22:55

score 68 · Answer 2 · 2021-10-06 10:48:27

68

Views

Are $1+\exp(-B_{1}^2)$ and $\inf\{t \geq 0 : B_t \geq W_t + \exp(-t)\}$ stopping times?

Published on 06 Oct 2021 - 10:48

score 145 · Answer 3 · 2021-10-12 11:06:10

145

Views

Show that the hitting time of a closed set is stopping time

Published on 12 Oct 2021 - 11:06

score 132 · Answer 4 · 2021-10-12 16:09:08

132

Views

If $X$ is a Lévy process, is $\tau_n:=\inf\left\{t\ge\tau_{n-1}:\left\|X_t-X_{\tau_{n-1}}\right\|_E\ge c\right\}$ independent identically distributed?

Published on 12 Oct 2021 - 16:09

score 20 · Answer 5 · 2026-03-27 13:02:00

20

Views

If the jumps of a path $x$ are bounded by $c$, how do we show that implies $\|x(t)\|\ge2c$ implies $\inf\{s:\|x(s)\|\ge c\}<t$

Published on 27 Mar 2026 - 13:02

score 218 · Answer 6 · 2021-10-13 01:09:57

218

Views

Whether the optional stopping theorem is true for a positive continuous martingale and integrable stopping times

Published on 13 Oct 2021 - 1:09

score 585 · Answer 7 · 2021-10-14 12:51:14

585

Views

Toss a coin until you get $n$ heads in a row. Expected number of tails tossed?

Published on 14 Oct 2021 - 12:51

score 138 · Answer 8 · 2026-03-27 13:01:58

138

Views

If $x:[0,\infty)\to E$ is càdlàg and $\tau_0:=0$, show that $\inf\left\{t>\tau_{n-1}:\Delta x(t)\in B\right\}\xrightarrow{n\to\infty}\infty$

Published on 27 Mar 2026 - 13:01

score 174 · Answer 9 · 2026-03-29 21:37:35

174

Views

Probability of hitting time conditional on the last step of Simple random walk.

Published on 29 Mar 2026 - 21:37

score 128 · Answer 10 · 2026-03-27 13:01:58

128

Views

How do we show that the jumping times $\inf\{t:\Delta X_t\in B\}$ of a Lévy process $X$ are stopping times?

Published on 27 Mar 2026 - 13:01

score 171 · Answer 11 · 2021-10-25 03:08:38

171

Views

Prove that $ P(T>n)=P\left(X_{n}>Y_{n}\right)-P\left(X_{n}<Y_{n}\right) $

Published on 25 Oct 2021 - 3:08

score 225 · Answer 12 · 2026-03-27 14:30:42

225

Views

Distribution of a stochastic process at a stopping time.

Published on 27 Mar 2026 - 14:30

score 84 · Answer 13 · 2021-10-31 11:13:48

84

Views

Is $\inf\{t>0:\Delta\omega(t)\in B\}$ a stopping time on the canonical path space?

Published on 31 Oct 2021 - 11:13

score 946 · Answer 14 · 2021-11-01 13:46:45

946

Views

Showing that a stopping time is finite for a biased random walk.

Published on 01 Nov 2021 - 13:46

score 69 · Answer 15 · 2021-11-03 21:15:32

69

Views

Interpretation of Stopped $\sigma$-algebra

Published on 03 Nov 2021 - 21:15

List Question

Iterated optional times

Are $1+\exp(-B_{1}^2)$ and $\inf\{t \geq 0 : B_t \geq W_t + \exp(-t)\}$ stopping times?

Show that the hitting time of a closed set is stopping time

If $X$ is a Lévy process, is $\tau_n:=\inf\left\{t\ge\tau_{n-1}:\left\|X_t-X_{\tau_{n-1}}\right\|_E\ge c\right\}$ independent identically distributed?

If the jumps of a path $x$ are bounded by $c$, how do we show that implies $\|x(t)\|\ge2c$ implies $\inf\{s:\|x(s)\|\ge c\}<t$

Whether the optional stopping theorem is true for a positive continuous martingale and integrable stopping times

Toss a coin until you get $n$ heads in a row. Expected number of tails tossed?

If $x:[0,\infty)\to E$ is càdlàg and $\tau_0:=0$, show that $\inf\left\{t>\tau_{n-1}:\Delta x(t)\in B\right\}\xrightarrow{n\to\infty}\infty$

Probability of hitting time conditional on the last step of Simple random walk.

How do we show that the jumping times $\inf\{t:\Delta X_t\in B\}$ of a Lévy process $X$ are stopping times?

Prove that $ P(T>n)=P\left(X_{n}>Y_{n}\right)-P\left(X_{n}<Y_{n}\right) $

Distribution of a stochastic process at a stopping time.

Is $\inf\{t>0:\Delta\omega(t)\in B\}$ a stopping time on the canonical path space?

Showing that a stopping time is finite for a biased random walk.

Interpretation of Stopped $\sigma$-algebra

Trending Questions

Popular # Hahtags

Popular Questions