Question

Covariance of two Brownian motion integrals

score 215 · Answer 1 · 2026-03-26 06:30:17

215

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Covariance of two Brownian motion integrals

Published on 26 Mar 2026 - 6:30

score 189 · Answer 2 · 2019-03-25 03:42:55

189

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Let $M(b)=\lim_{n\rightarrow\infty}\sum_{k=n+1}^{2n} \{b^k x\}/k$. Do we have $\int_{1}^{2}M(b)db = 1/4$?

Published on 25 Mar 2019 - 3:42

score 306 · Answer 3 · 2026-03-25 09:53:47

306

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How to write a system of stochastic differential equations (SDE) mathematically correct?

Published on 25 Mar 2026 - 9:53

score 97 · Answer 4 · 2026-03-26 22:18:08

97

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Decay rate of a birth-death Markov chain and relationship with the support of the orthogonalizing probability

Published on 26 Mar 2026 - 22:18

score 94 · Answer 5 · 2026-04-03 14:53:33

94

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Strict stochastic domination of "thinned out" random cluster model

Published on 03 Apr 2026 - 14:53

score 34 · Answer 6 · 2026-03-28 00:50:19

34

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Does $\{X_n\}_{n = 1}^\infty$ being a supermartingale imply $P(\sup_{1 \leq k \leq n} X_k \geq a) \leq \frac{E(\max\{0, X_n\}) - E(X_n) + EX_1)}{a}$?

Published on 28 Mar 2026 - 0:50

score 44 · Answer 7 · 2026-03-28 11:25:21

44

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Why do we want probability spaces and filtrations to be complete?

Published on 28 Mar 2026 - 11:25

score 2.8k · Answer 8 · 2026-03-26 06:30:06

2.8k

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Variance of Stochastic Integral $\int_0^1{t^2 dWt}$

Published on 26 Mar 2026 - 6:30

score 79 · Answer 9 · 2019-03-26 21:21:38

79

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Why does randomly counting the logarithm succeed with high probability?

Published on 26 Mar 2019 - 21:21

score 266 · Answer 10 · 2026-03-30 08:33:07

266

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Sum of elements of the eigenvalue of a Markov Chain.

Published on 30 Mar 2026 - 8:33

score 645 · Answer 11 · 2026-03-26 04:49:37

645

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Poisson Process with Expected Time (Stochastic Processes)

Published on 26 Mar 2026 - 4:49

score 203 · Answer 12 · 2026-03-24 23:29:23

203

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Looking for intriguing applications of martingales

Published on 24 Mar 2026 - 23:29

score 59 · Answer 13 · 2026-03-26 06:29:44

59

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Let $\{X_t ,t\ge0\} $ be Poisson process with parameter $\lambda $ and arrival time $T_1,T_2,\cdots$ , Find $Var(T_2-t|X_t=1)$

Published on 26 Mar 2026 - 6:29

score 269 · Answer 14 · 2026-03-26 20:40:07

269

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Brownian motion remains nonnegative for some interval with length $1$ almost surely

Published on 26 Mar 2026 - 20:40

score 87 · Answer 15 · 2026-03-25 20:35:59

87

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Mistake on Wikipedia: Completeness of Filtration and Completeness of Individual Probability Spaces

Published on 25 Mar 2026 - 20:35

List Question

Covariance of two Brownian motion integrals

Let $M(b)=\lim_{n\rightarrow\infty}\sum_{k=n+1}^{2n} \{b^k x\}/k$. Do we have $\int_{1}^{2}M(b)db = 1/4$?

How to write a system of stochastic differential equations (SDE) mathematically correct?

Decay rate of a birth-death Markov chain and relationship with the support of the orthogonalizing probability

Strict stochastic domination of "thinned out" random cluster model

Does $\{X_n\}_{n = 1}^\infty$ being a supermartingale imply $P(\sup_{1 \leq k \leq n} X_k \geq a) \leq \frac{E(\max\{0, X_n\}) - E(X_n) + EX_1)}{a}$?

Why do we want probability spaces and filtrations to be complete?

Variance of Stochastic Integral $\int_0^1{t^2 dWt}$

Why does randomly counting the logarithm succeed with high probability?

Sum of elements of the eigenvalue of a Markov Chain.

Poisson Process with Expected Time (Stochastic Processes)

Looking for intriguing applications of martingales

Let $\{X_t ,t\ge0\} $ be Poisson process with parameter $\lambda $ and arrival time $T_1,T_2,\cdots$ , Find $Var(T_2-t|X_t=1)$

Brownian motion remains nonnegative for some interval with length $1$ almost surely

Mistake on Wikipedia: Completeness of Filtration and Completeness of Individual Probability Spaces

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