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Stochastic Processes, practice problem taken from One Thousand Exercises in Probability

score 178 · Answer 1 · 2026-04-10 23:24:51

178

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Stochastic Processes, practice problem taken from One Thousand Exercises in Probability

Published on 10 Apr 2026 - 23:24

score 394 · Answer 2 · 2026-04-11 04:26:20

394

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Is a continuous locally square-integrable martingale uniquely (in distribution) determined by its angle bracket?

Published on 11 Apr 2026 - 4:26

score 92 · Answer 3 · 2026-04-08 01:15:27

92

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Why is $\sup_{n \in \mathbb{N}} E[|X_n|^p] \leq B < \infty$ different from $\sup_{n \in \mathbb{N}} E[|X_n|^p] < \infty$ as a requirement?

Published on 08 Apr 2026 - 1:15

score 972 · Answer 4 · 2021-02-24 15:42:00

972

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Why is $\frac{Z_n}{\mu^n}$ a martingale? (Galton-Watson Process.)

Published on 24 Feb 2021 - 15:42

score 184 · Answer 5 · 2026-04-11 22:36:00

184

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Is the Radon Nikodym derivative conditioned on a filtration monotonically increasing?

Published on 11 Apr 2026 - 22:36

score 59 · Answer 6 · 2021-02-24 19:08:10

59

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Using Martingales to find expected values.

Published on 24 Feb 2021 - 19:08

score 239 · Answer 7 · 2021-02-25 05:26:23

239

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Why does the Galton-Watson Process dies out a.s. when the mean is less than 1?

Published on 25 Feb 2021 - 5:26

score 416 · Answer 8 · 2021-02-25 07:33:47

416

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If $X_n$ is an $L_1$-bounded martingale, show that $\sum_n(X_n-X_{n-1})^2< \infty$ a.s.

Published on 25 Feb 2021 - 7:33

score 121 · Answer 9 · 2026-03-28 10:02:13

121

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Connection between elliptic operators, the Martingale problem and diffusion

Published on 28 Mar 2026 - 10:02

score 185 · Answer 10 · 2026-04-11 13:14:42

185

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Question about how to use martingale decomposition to bound the variance of a random variable.

Published on 11 Apr 2026 - 13:14

score 200 · Answer 11 · 2026-04-11 19:48:13

200

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Control the sum of the square of martingale increments

Published on 11 Apr 2026 - 19:48

score 834 · Answer 12 · 2026-04-11 00:19:03

834

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Expectation of a martingale

Published on 11 Apr 2026 - 0:19

score 77 · Answer 13 · 2026-04-07 07:47:44

77

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Tossing a coin with time evolving bias

Published on 07 Apr 2026 - 7:47

score 384 · Answer 14 · 2026-04-09 18:46:22

384

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For a cadlag submartingale $X$ the function $t \mapsto E[X_{t}]$ is right continuous.

Published on 09 Apr 2026 - 18:46

score 331 · Answer 15 · 2026-04-10 08:58:50

331

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How to prove autocorrelation function converges in distribution to normal distribution

Published on 10 Apr 2026 - 8:58

List Question

Stochastic Processes, practice problem taken from One Thousand Exercises in Probability

Is a continuous locally square-integrable martingale uniquely (in distribution) determined by its angle bracket?

Why is $\sup_{n \in \mathbb{N}} E[|X_n|^p] \leq B < \infty$ different from $\sup_{n \in \mathbb{N}} E[|X_n|^p] < \infty$ as a requirement?

Why is $\frac{Z_n}{\mu^n}$ a martingale? (Galton-Watson Process.)

Is the Radon Nikodym derivative conditioned on a filtration monotonically increasing?

Using Martingales to find expected values.

Why does the Galton-Watson Process dies out a.s. when the mean is less than 1?

If $X_n$ is an $L_1$-bounded martingale, show that $\sum_n(X_n-X_{n-1})^2< \infty$ a.s.

Connection between elliptic operators, the Martingale problem and diffusion

Question about how to use martingale decomposition to bound the variance of a random variable.

Control the sum of the square of martingale increments

Expectation of a martingale

Tossing a coin with time evolving bias

For a cadlag submartingale $X$ the function $t \mapsto E[X_{t}]$ is right continuous.

How to prove autocorrelation function converges in distribution to normal distribution

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