Question

Why do we have $\{T\leq t\}=\bigcap_{n \in \mathbb{N}}\bigcup_{s \in \mathbb{Q}\cap[0,t]}\{X_s\leq c+n^{-1}\} \in \mathcal{F}_t $?

score 37 · Answer 1 · 2021-06-05 15:40:28

37

Views

Why do we have $\{T\leq t\}=\bigcap_{n \in \mathbb{N}}\bigcup_{s \in \mathbb{Q}\cap[0,t]}\{X_s\leq c+n^{-1}\} \in \mathcal{F}_t $?

Published on 05 Jun 2021 - 15:40

score 72 · Answer 2 · 2021-06-08 15:32:00

72

Views

$\mathbb{E}[M_{\tau+\theta}M_{\tau}]=\mathbb{E}[M_{\tau}^2]$

Published on 08 Jun 2021 - 15:32

score 190 · Answer 3 · 2021-06-08 21:51:53

190

Views

If $X$ is a supermartingale and $S$ a bounded stopping times, then so is the stopped process $X^S$.

Published on 08 Jun 2021 - 21:51

score 33 · Answer 4 · 2021-06-09 09:11:56

33

Views

Stochastic processes and Markov chains

Published on 09 Jun 2021 - 9:11

score 188 · Answer 5 · 2021-06-10 17:06:10

188

Views

Brownian motion with drift between two boundaries

Published on 10 Jun 2021 - 17:06

score 170 · Answer 6 · 2026-03-27 00:58:59

170

Views

Let $\sigma,\tau$ be stopping times. $\{\sigma<\tau\}\in\mathcal{F}_{\sigma}$?

Published on 27 Mar 2026 - 0:58

score 26 · Answer 7 · 2021-06-12 14:26:59

26

Views

Is $A \cap \{\tau > t\} \in \mathcal{F}_{t}$?

Published on 12 Jun 2021 - 14:26

score 57 · Answer 8 · 2021-06-17 18:17:38

57

Views

Probability of hitting time to be equal to particular $t$.

Published on 17 Jun 2021 - 18:17

score 83 · Answer 9 · 2026-03-31 12:03:39

83

Views

Expectation of the product of a stopping time and a stochastic process

Published on 31 Mar 2026 - 12:03

score 109 · Answer 10 · 2021-06-21 21:49:55

109

Views

Discontinuities in the expectation of a stopping time (Bayesian coin-tossing)

Published on 21 Jun 2021 - 21:49

score 45 · Answer 11 · 2021-07-01 19:45:14

45

Views

If $x:[0,T]\to E$ is continuous and $Ω⊆E$ is open with $x(0)\in Ω$, how are $\inf\{t∈[0,T]:x(t)\not\in Ω\}$ and $\sup\{t∈(0,T]:x([0,t])⊆Ω\}$ related?

Published on 01 Jul 2021 - 19:45

score 67 · Answer 12 · 2021-07-04 05:29:19

67

Views

Computing a conditional probability using a martingle

Published on 04 Jul 2021 - 5:29

score 390 · Answer 13 · 2021-07-07 16:06:56

390

Views

Expectation of integration Brownian motion at stopping time.

Published on 07 Jul 2021 - 16:06

score 373 · Answer 14 · 2021-07-13 23:30:48

373

Views

Stopping time random walk in a circle

Published on 13 Jul 2021 - 23:30

score 162 · Answer 15 · 2021-07-19 09:45:33

162

Views

What's the expected cover time of an asymmetric random walk on a circle?

Published on 19 Jul 2021 - 9:45

List Question

Why do we have $\{T\leq t\}=\bigcap_{n \in \mathbb{N}}\bigcup_{s \in \mathbb{Q}\cap[0,t]}\{X_s\leq c+n^{-1}\} \in \mathcal{F}_t $?

$\mathbb{E}[M_{\tau+\theta}M_{\tau}]=\mathbb{E}[M_{\tau}^2]$

If $X$ is a supermartingale and $S$ a bounded stopping times, then so is the stopped process $X^S$.

Stochastic processes and Markov chains

Brownian motion with drift between two boundaries

Let $\sigma,\tau$ be stopping times. $\{\sigma<\tau\}\in\mathcal{F}_{\sigma}$?

Is $A \cap \{\tau > t\} \in \mathcal{F}_{t}$?

Probability of hitting time to be equal to particular $t$.

Expectation of the product of a stopping time and a stochastic process

Discontinuities in the expectation of a stopping time (Bayesian coin-tossing)

If $x:[0,T]\to E$ is continuous and $Ω⊆E$ is open with $x(0)\in Ω$, how are $\inf\{t∈[0,T]:x(t)\not\in Ω\}$ and $\sup\{t∈(0,T]:x([0,t])⊆Ω\}$ related?

Computing a conditional probability using a martingle

Expectation of integration Brownian motion at stopping time.

Stopping time random walk in a circle

What's the expected cover time of an asymmetric random walk on a circle?

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