Question

Stopped running sum of uniform random variables $\sum_{j=1}^k\frac{X_j}{2^j}$

score 135 · Answer 1 · 2022-12-19 20:06:30

135

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Stopped running sum of uniform random variables $\sum_{j=1}^k\frac{X_j}{2^j}$

Published on 19 Dec 2022 - 20:06

score 41 · Answer 2 · 2022-12-21 02:15:51

41

Views

A construction of permuted stochastic sequences

Published on 21 Dec 2022 - 2:15

score 67 · Answer 3 · 2022-12-21 13:45:45

67

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Calculating $\mathbb E\left[\sum_{k=1}^TX_k\right]$ where $(X_k)$ where $T$ is a stopping time

Published on 21 Dec 2022 - 13:45

score 169 · Answer 4 · 2022-12-27 22:21:19

169

Views

Randomised stopping time

Published on 27 Dec 2022 - 22:21

score 73 · Answer 5 · 2023-01-03 23:41:51

73

Views

A useful criterion on stopping times

Published on 03 Jan 2023 - 23:41

score 45 · Answer 6 · 2023-01-04 21:25:11

45

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Optimal Online Search Problem

Published on 04 Jan 2023 - 21:25

score 187 · Answer 7 · 2026-03-27 12:20:02

187

Views

$\sigma$-algebra of $\tau$-past: Definition vs interpretation

Published on 27 Mar 2026 - 12:20

score 120 · Answer 8 · 2023-01-07 08:56:12

120

Views

Stopping time max $\{n: \ X_1 + \cdots + X_n \le t \}$

Published on 07 Jan 2023 - 8:56

score 80 · Answer 9 · 2026-03-27 07:50:32

80

Views

Showing that the stopped filtration $\mathcal{F}_{s \wedge t} = \mathcal{F}_s \cap \mathcal{F}_t$

Published on 27 Mar 2026 - 7:50

score 41 · Answer 10 · 2026-03-27 13:48:17

41

Views

$A\in F_\tau\land\tau(\omega)<\infty\Rightarrow A\in F_{\tau(\omega)}$

Published on 27 Mar 2026 - 13:48

score 45 · Answer 11 · 2026-03-27 10:47:49

45

Views

Showing that the stopped filtration $\mathcal{F}_{s \vee t} = \mathcal{F}_s \cup \mathcal{F}_t$

Published on 27 Mar 2026 - 10:47

score 73 · Answer 12 · 2023-01-09 16:47:37

73

Views

Measurable Projection Theorem and the Debut Theorem

Published on 09 Jan 2023 - 16:47

score 153 · Answer 13 · 2026-04-02 02:14:03

153

Views

Find probability distribution of stopping time consisting of a two-sided barrior and a time constrained for Brownian motion with drift?

Published on 02 Apr 2026 - 2:14

score 366 · Answer 14 · 2023-01-16 16:14:52

366

Views

Intuition behind Filtrations, Martingales and Stopping times

Published on 16 Jan 2023 - 16:14

score 37 · Answer 15 · 2023-01-16 16:53:59

37

Views

A random variable $Y$ is $\mathcal F_T$-measurable IFF $Y1_{\{T=n\}}$ is $\mathcal F_n$-measurable for all $n \in \mathbb N$

Published on 16 Jan 2023 - 16:53

List Question

Stopped running sum of uniform random variables $\sum_{j=1}^k\frac{X_j}{2^j}$

A construction of permuted stochastic sequences

Calculating $\mathbb E\left[\sum_{k=1}^TX_k\right]$ where $(X_k)$ where $T$ is a stopping time

Randomised stopping time

A useful criterion on stopping times

Optimal Online Search Problem

$\sigma$-algebra of $\tau$-past: Definition vs interpretation

Stopping time max $\{n: \ X_1 + \cdots + X_n \le t \}$

Showing that the stopped filtration $\mathcal{F}_{s \wedge t} = \mathcal{F}_s \cap \mathcal{F}_t$

$A\in F_\tau\land\tau(\omega)<\infty\Rightarrow A\in F_{\tau(\omega)}$

Showing that the stopped filtration $\mathcal{F}_{s \vee t} = \mathcal{F}_s \cup \mathcal{F}_t$

Measurable Projection Theorem and the Debut Theorem

Find probability distribution of stopping time consisting of a two-sided barrior and a time constrained for Brownian motion with drift?

Intuition behind Filtrations, Martingales and Stopping times

A random variable $Y$ is $\mathcal F_T$-measurable IFF $Y1_{\{T=n\}}$ is $\mathcal F_n$-measurable for all $n \in \mathbb N$

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