Question

Understanding how to formally use the definition of stopping time to prove something is a stopping time

score 342 · Answer 1 · 2026-03-28 16:25:54

342

Views

Understanding how to formally use the definition of stopping time to prove something is a stopping time

Published on 28 Mar 2026 - 16:25

score 43 · Answer 2 · 2026-03-28 16:20:45

43

Views

chance of getting AB before AA

Published on 28 Mar 2026 - 16:20

score 115 · Answer 3 · 2023-06-21 19:06:22

115

Views

Choquet-Deny theorem

Published on 21 Jun 2023 - 19:06

score 59 · Answer 4 · 2026-03-31 03:28:04

59

Views

Regularity of continuous martingales

Published on 31 Mar 2026 - 3:28

score 42 · Answer 5 · 2023-06-24 13:58:36

42

Views

Switching principle for continuous time martingale?

Published on 24 Jun 2023 - 13:58

score 86 · Answer 6 · 2026-03-28 20:06:17

86

Views

Showing that $\exp(rN_t-\lambda t(e^r-1))$ is a Martingale

Published on 28 Mar 2026 - 20:06

score 81 · Answer 7 · 2026-03-30 07:09:23

81

Views

Verification of the hypotheses and application of Doobs' optional stopping theorem to 2D simple symmetric random walk

Published on 30 Mar 2026 - 7:09

score 62 · Answer 8 · 2023-06-28 17:56:34

62

Views

Average time a light bulb is lit

Published on 28 Jun 2023 - 17:56

score 95 · Answer 9 · 2023-06-29 09:16:42

95

Views

An $L^2 $ martingale $M_n$ is bounded in $L^2$ if and only if $\sum_{k=1}^{\infty} E[M_k-M_{k-1}]^2 < \infty$

Published on 29 Jun 2023 - 9:16

score 125 · Answer 10 · 2026-03-26 11:06:52

125

Views

Prove Bernstein’s inequality for martingales

Published on 26 Mar 2026 - 11:06

score 36 · Answer 11 · 2023-06-30 23:07:15

36

Views

Why can one get rid of a conditioning sigma-algebra by independence by setting another sigma-measurable variable equal to a constant?

Published on 30 Jun 2023 - 23:07

score 77 · Answer 12 · 2023-07-01 08:22:35

77

Views

Prove $Y_i = \frac{2X_i-i}{2n-i}, (1\le i \le 2n-1)$ is a martingale

Published on 01 Jul 2023 - 8:22

score 48 · Answer 13 · 2023-07-01 11:50:12

48

Views

Prove $Z_i = \frac{2n-i}{2n-i-1}Y_i^2 - \frac1{2n-i-1} (1 \le i \le 2n-2) $ is a martingale

Published on 01 Jul 2023 - 11:50

score 22 · Answer 14 · 2023-07-02 00:30:23

22

Views

Prove that $Z_n=(\frac{a}{b})^{\sum_{j=1}^n\xi_j}(\frac{1-a}{1-b})^{n-\sum_{j=1}^n\xi_j}$ is a martingale

Published on 02 Jul 2023 - 0:30

score 86 · Answer 15 · 2023-07-02 08:21:41

86

Views

Show $Q(\eta_n) := \mathbb P \{\exists m < \infty : \eta_m = 0 |\eta_0 = \eta_n\}$ is a martingale

Published on 02 Jul 2023 - 8:21

List Question

Understanding how to formally use the definition of stopping time to prove something is a stopping time

chance of getting AB before AA

Choquet-Deny theorem

Regularity of continuous martingales

Switching principle for continuous time martingale?

Showing that $\exp(rN_t-\lambda t(e^r-1))$ is a Martingale

Verification of the hypotheses and application of Doobs' optional stopping theorem to 2D simple symmetric random walk

Average time a light bulb is lit

An $L^2 $ martingale $M_n$ is bounded in $L^2$ if and only if $\sum_{k=1}^{\infty} E[M_k-M_{k-1}]^2 < \infty$

Prove Bernstein’s inequality for martingales

Why can one get rid of a conditioning sigma-algebra by independence by setting another sigma-measurable variable equal to a constant?

Prove $Y_i = \frac{2X_i-i}{2n-i}, (1\le i \le 2n-1)$ is a martingale

Prove $Z_i = \frac{2n-i}{2n-i-1}Y_i^2 - \frac1{2n-i-1} (1 \le i \le 2n-2) $ is a martingale

Prove that $Z_n=(\frac{a}{b})^{\sum_{j=1}^n\xi_j}(\frac{1-a}{1-b})^{n-\sum_{j=1}^n\xi_j}$ is a martingale

Show $Q(\eta_n) := \mathbb P \{\exists m < \infty : \eta_m = 0 |\eta_0 = \eta_n\}$ is a martingale

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