Question

For a Brownian motion $B(t)$, show $0=\mathbb E[ B(\tau)]$ where $\tau := \max \{\tau_a, \tau_b\}$ is the latter hitting time of the levels $a<0<b$.

score 322 · Answer 1 · 2020-10-27 02:47:00

322

Views

For a Brownian motion $B(t)$, show $0=\mathbb E[ B(\tau)]$ where $\tau := \max \{\tau_a, \tau_b\}$ is the latter hitting time of the levels $a<0<b$.

Published on 27 Oct 2020 - 2:47

score 42 · Answer 2 · 2020-10-27 14:22:41

42

Views

$\mathbb{E}[M_{a}]\geq \mathbb{E}[M_{b}]$ with $a,b$ limited stopping times and $M$ sub-martingale

Published on 27 Oct 2020 - 14:22

score 88 · Answer 3 · 2020-10-28 17:47:36

88

Views

Regarding the Maximum of Two Stopping Times

Published on 28 Oct 2020 - 17:47

score 92 · Answer 4 · 2020-10-31 02:35:43

92

Views

Show that $\mathbb{P}(\tau<\infty)=1$ where $\tau:=\inf \{n\geq 1\::\:|S_{n}|=N \}$ and $\{S_{n}\}$ is a symmetric Random Walk in $\mathbb{Z}$

Published on 31 Oct 2020 - 2:35

score 314 · Answer 5 · 2020-10-31 17:08:48

314

Views

memorylessness of geometric distribution

Published on 31 Oct 2020 - 17:08

score 56 · Answer 6 · 2020-11-01 22:57:30

56

Views

Inequality regarding the Brownian motion stopping time

Published on 01 Nov 2020 - 22:57

score 59 · Answer 7 · 2020-11-02 14:36:15

59

Views

Is $n 1_A$ a stopping time?

Published on 02 Nov 2020 - 14:36

score 73 · Answer 8 · 2026-03-26 21:07:12

73

Views

Throw dice till numbers are the same

Published on 26 Mar 2026 - 21:07

score 93 · Answer 9 · 2020-11-04 22:41:21

93

Views

Is intersection a stopping time?

Published on 04 Nov 2020 - 22:41

score 52 · Answer 10 · 2020-11-11 01:04:26

52

Views

Divergent Stopping Times

Published on 11 Nov 2020 - 1:04

score 20 · Answer 11 · 2020-11-13 08:05:50

20

Views

$t\mapsto\tau(\omega)\land t$ continuous?

Published on 13 Nov 2020 - 8:05

score 120 · Answer 12 · 2020-11-13 08:31:59

120

Views

Brownian Motion Hitting Time of functions $y=t$ and $y=t^2$

Published on 13 Nov 2020 - 8:31

score 50 · Answer 13 · 2020-11-14 13:29:18

50

Views

Hitting set expected value

Published on 14 Nov 2020 - 13:29

score 51 · Answer 14 · 2020-11-21 11:36:20

51

Views

stopping times (definition)

Published on 21 Nov 2020 - 11:36

score 40 · Answer 15 · 2020-11-23 13:50:45

40

Views

Random Walk in $\mathbb{R}^2$, $R_n$ is distance from origin at time $n$, $\tau=\text{inf}\{n:R_n>r\}.$ Show that $\mathbb{E}(\tau)<\infty$

Published on 23 Nov 2020 - 13:50

List Question

For a Brownian motion $B(t)$, show $0=\mathbb E[ B(\tau)]$ where $\tau := \max \{\tau_a, \tau_b\}$ is the latter hitting time of the levels $a<0<b$.

$\mathbb{E}[M_{a}]\geq \mathbb{E}[M_{b}]$ with $a,b$ limited stopping times and $M$ sub-martingale

Regarding the Maximum of Two Stopping Times

Show that $\mathbb{P}(\tau<\infty)=1$ where $\tau:=\inf \{n\geq 1\::\:|S_{n}|=N \}$ and $\{S_{n}\}$ is a symmetric Random Walk in $\mathbb{Z}$

memorylessness of geometric distribution

Inequality regarding the Brownian motion stopping time

Is $n 1_A$ a stopping time?

Throw dice till numbers are the same

Is intersection a stopping time?

Divergent Stopping Times

$t\mapsto\tau(\omega)\land t$ continuous?

Brownian Motion Hitting Time of functions $y=t$ and $y=t^2$

Hitting set expected value

stopping times (definition)

Random Walk in $\mathbb{R}^2$, $R_n$ is distance from origin at time $n$, $\tau=\text{inf}\{n:R_n>r\}.$ Show that $\mathbb{E}(\tau)<\infty$

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