Question

Show $\limsup _{t \to \infty} \frac{B_t}{\sqrt{t \ln t}} \leq 1 $ using the fact that $\frac{e^{B_t ^2 / (1+2t)}}{\sqrt{1+2t}}$ is a martingale.

score 486 · Answer 1 · 2026-04-16 04:07:40

486

Views

Show $\limsup _{t \to \infty} \frac{B_t}{\sqrt{t \ln t}} \leq 1 $ using the fact that $\frac{e^{B_t ^2 / (1+2t)}}{\sqrt{1+2t}}$ is a martingale.

Published on 16 Apr 2026 - 4:07

score 46 · Answer 2 · 2026-04-11 22:29:01

46

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what's the integral of $(-\ln(x))^a$

Published on 11 Apr 2026 - 22:29

score 522 · Answer 3 · 2026-04-15 11:27:54

522

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score 18 · Answer 4 · 2026-04-12 13:02:32

18

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score 1.1k · Answer 5 · 2026-04-12 10:15:52

1.1k

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score 116 · Answer 6 · 2026-04-14 07:33:43

116

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score 178 · Answer 7 · 2026-04-13 21:06:50

178

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score 374 · Answer 8 · 2026-04-21 15:49:54

374

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score 843 · Answer 9 · 2026-04-14 22:01:46

843

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222

Views

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score 123 · Answer 11 · 2026-04-10 15:39:35

123

Views

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score 50 · Answer 12 · 2026-04-14 07:42:13

50

Views

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Published on 14 Apr 2026 - 7:42

score 151 · Answer 13 · 2026-04-15 23:45:58

151

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Published on 15 Apr 2026 - 23:45

score 142 · Answer 14 · 2026-04-14 18:46:24

142

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score 542 · Answer 15 · 2026-04-13 02:07:14

542

Views

Durret problem 4.8.3 - Random walk and optional sampling theorem application

Published on 13 Apr 2026 - 2:07

List Question

Show $\limsup _{t \to \infty} \frac{B_t}{\sqrt{t \ln t}} \leq 1 $ using the fact that $\frac{e^{B_t ^2 / (1+2t)}}{\sqrt{1+2t}}$ is a martingale.

what's the integral of $(-\ln(x))^a$

Find the proportion of points that are won by player 1

Conditional expectation when each of the random variables have the same density?

Definition of sample path of stochastic process

A coin game and a crazy recurrence

How to get the value Expectation for the Ornstein Uhlenback?

Proof clarification: Slepian’s inequality

Two Poisson Process related together

Cinlar, Probability and Stochastic, Ch.2 ex. 4.14

Trouble Understanding Proof: Proving Chain is Markov Chain

The Expectation of $e^{W_{t}+W_{s}} $ for fixed t and s

Continuity of the stochastic process $X_t=\int_{0}^{t}(a+b\frac{u^n}{t^n} ) dW_{u} $

Why is the expected value of $E(MX|M=X) \neq E(X^2)$

Durret problem 4.8.3 - Random walk and optional sampling theorem application

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