Question

Show that $\mathbb E[\exp(-\lambda(T_{a}\land T_{b}))]=\cosh(\frac{a+b}{2}\sqrt{2\lambda})/\cosh(\frac{a-b}{2}\sqrt{2\lambda})$

score 293 · Answer 1 · 2021-11-05 17:40:51

293

Views

Show that $\mathbb E[\exp(-\lambda(T_{a}\land T_{b}))]=\cosh(\frac{a+b}{2}\sqrt{2\lambda})/\cosh(\frac{a-b}{2}\sqrt{2\lambda})$

Published on 05 Nov 2021 - 17:40

score 131 · Answer 2 · 2021-11-07 09:53:22

131

Views

Stopping time build by 'filtration'-Brownian motion

Published on 07 Nov 2021 - 9:53

score 168 · Answer 3 · 2021-11-10 02:25:04

168

Views

A Markov Chain ($Y_n$) based on the stopping time of another Markov Chain $X_n$

Published on 10 Nov 2021 - 2:25

score 31 · Answer 4 · 2021-11-10 16:32:04

31

Views

Is it possible to recover the fact that $\mathbb P(T_{a} < T_{b} ) = b/(b-a)$ using $\mathbb E[ e^{-\lambda T_{a}}\chi_{\{T_{a}< T_{b}\}}]$

Published on 10 Nov 2021 - 16:32

score 626 · Answer 5 · 2021-11-11 23:31:56

626

Views

Difference of two stopping times

Published on 11 Nov 2021 - 23:31

score 44 · Answer 6 · 2021-11-13 01:00:33

44

Views

How does $\{S\wedge t \leq T \wedge t\}$ help here?

Published on 13 Nov 2021 - 1:00

score 78 · Answer 7 · 2021-11-15 21:22:17

78

Views

How to show that $n1_E + m1_{\Omega \setminus E}$ is a stopping time for $E\in\mathcal{F}_n$?

Published on 15 Nov 2021 - 21:22

score 284 · Answer 8 · 2026-03-31 22:53:42

284

Views

First Passage Time distribution for a 2D Brownian particle with constant drift

Published on 31 Mar 2026 - 22:53

score 77 · Answer 9 · 2021-11-18 14:01:37

77

Views

Reference for a stopping-time problem

Published on 18 Nov 2021 - 14:01

score 123 · Answer 10 · 2021-11-19 09:36:49

123

Views

biased simple random walk and optional stopping theorem

Published on 19 Nov 2021 - 9:36

score 66 · Answer 11 · 2021-11-21 16:22:25

66

Views

$\tau=s \mathbf{1}_{A^c}+t\mathbf{1}_A$, $A \in \mathcal F_s$ is a stopping time

Published on 21 Nov 2021 - 16:22

score 36 · Answer 12 · 2021-11-25 10:12:19

36

Views

Why is this process bounded?

Published on 25 Nov 2021 - 10:12

score 173 · Answer 13 · 2021-11-29 06:17:55

173

Views

Conditions on stopping time being finite

Published on 29 Nov 2021 - 6:17

score 66 · Answer 14 · 2021-12-04 13:58:20

66

Views

show that the limit of a continuous time process with discrete values is a martingale

Published on 04 Dec 2021 - 13:58

score 153 · Answer 15 · 2026-03-28 09:33:34

153

Views

Optimal stopping of a Poisson Process with a risky reward

Published on 28 Mar 2026 - 9:33

List Question

Show that $\mathbb E[\exp(-\lambda(T_{a}\land T_{b}))]=\cosh(\frac{a+b}{2}\sqrt{2\lambda})/\cosh(\frac{a-b}{2}\sqrt{2\lambda})$

Stopping time build by 'filtration'-Brownian motion

A Markov Chain ($Y_n$) based on the stopping time of another Markov Chain $X_n$

Is it possible to recover the fact that $\mathbb P(T_{a} < T_{b} ) = b/(b-a)$ using $\mathbb E[ e^{-\lambda T_{a}}\chi_{\{T_{a}< T_{b}\}}]$

Difference of two stopping times

How does $\{S\wedge t \leq T \wedge t\}$ help here?

How to show that $n1_E + m1_{\Omega \setminus E}$ is a stopping time for $E\in\mathcal{F}_n$?

First Passage Time distribution for a 2D Brownian particle with constant drift

Reference for a stopping-time problem

biased simple random walk and optional stopping theorem

$\tau=s \mathbf{1}_{A^c}+t\mathbf{1}_A$, $A \in \mathcal F_s$ is a stopping time

Why is this process bounded?

Conditions on stopping time being finite

show that the limit of a continuous time process with discrete values is a martingale

Optimal stopping of a Poisson Process with a risky reward

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