Question

Cumulative product of independent random variables with a stopping time

score 122 · Answer 1 · 2019-08-12 20:38:59

122

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Cumulative product of independent random variables with a stopping time

Published on 12 Aug 2019 - 20:38

score 134 · Answer 2 · 2019-08-14 15:25:43

134

Views

two sided brownian motion hit time +1 -1

Published on 14 Aug 2019 - 15:25

score 188 · Answer 3 · 2019-08-19 23:12:35

188

Views

Prove the following stopping time Cannot be a predictable stopping time.

Published on 19 Aug 2019 - 23:12

score 54 · Answer 4 · 2019-08-25 09:20:53

54

Views

Show that $T\boldsymbol 1_B+M\boldsymbol 1_{B^c}$ is a stopping time if $T$ is a stoping time.

Published on 25 Aug 2019 - 9:20

score 339 · Answer 5 · 2019-08-25 14:03:55

339

Views

If $T$ is a stopping time, prove that $X_T$ is $\mathcal F_T$ measurable.

Published on 25 Aug 2019 - 14:03

score 152 · Answer 6 · 2019-08-25 19:31:15

152

Views

Question about Doob's decomposition and a theorem in Durrett

Published on 25 Aug 2019 - 19:31

score 52 · Answer 7 · 2019-09-04 11:05:45

52

Views

Comparing geometric brownian motion at stopping time

Published on 04 Sep 2019 - 11:05

score 77 · Answer 8 · 2019-09-08 13:50:02

77

Views

Stopping time that is not a reaching time?

Published on 08 Sep 2019 - 13:50

score 156 · Answer 9 · 2019-09-09 13:10:56

156

Views

Expectation of the "truncated" partial sum of random variables

Published on 09 Sep 2019 - 13:10

score 134 · Answer 10 · 2019-09-09 14:50:00

134

Views

Show that the stopping moment $\tau$ is finite, find the distribution of $X_{\tau}$, calculate $\mathbb{E}e^{\tau}$.

Published on 09 Sep 2019 - 14:50

score 58 · Answer 11 · 2019-09-09 19:11:51

58

Views

Calculate $\mathbb{E} W_{\tau + 1}$, $\mathbb{E}W^{2}_{\tau+1}$ and $\mathbb{E}W_{\tau \land 5}$.

Published on 09 Sep 2019 - 19:11

score 161 · Answer 12 · 2019-09-10 09:09:42

161

Views

Expected value of the positive part of partial sum of random variables

Published on 10 Sep 2019 - 9:09

score 1.2k · Answer 13 · 2019-09-11 08:29:15

1.2k

Views

expected hitting time of asymmetric random walk

Published on 11 Sep 2019 - 8:29

score 64 · Answer 14 · 2019-09-13 07:08:48

64

Views

$\mathbb E[|X_T|]$ when $\mathbb E[T]<\infty$

Published on 13 Sep 2019 - 7:08

score 26 · Answer 15 · 2019-09-14 08:31:00

26

Views

Compute: Show that expected stopping times for $X_t = 2t + 3W_t$ and $Y_t = 6t + W_t$ to reach any any level $x>0$ are the same.

Published on 14 Sep 2019 - 8:31

List Question

Cumulative product of independent random variables with a stopping time

two sided brownian motion hit time +1 -1

Prove the following stopping time Cannot be a predictable stopping time.

Show that $T\boldsymbol 1_B+M\boldsymbol 1_{B^c}$ is a stopping time if $T$ is a stoping time.

If $T$ is a stopping time, prove that $X_T$ is $\mathcal F_T$ measurable.

Question about Doob's decomposition and a theorem in Durrett

Comparing geometric brownian motion at stopping time

Stopping time that is not a reaching time?

Expectation of the "truncated" partial sum of random variables

Show that the stopping moment $\tau$ is finite, find the distribution of $X_{\tau}$, calculate $\mathbb{E}e^{\tau}$.

Calculate $\mathbb{E} W_{\tau + 1}$, $\mathbb{E}W^{2}_{\tau+1}$ and $\mathbb{E}W_{\tau \land 5}$.

Expected value of the positive part of partial sum of random variables

expected hitting time of asymmetric random walk

$\mathbb E[|X_T|]$ when $\mathbb E[T]<\infty$

Compute: Show that expected stopping times for $X_t = 2t + 3W_t$ and $Y_t = 6t + W_t$ to reach any any level $x>0$ are the same.

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