Question

Let $\{X_n; n\geq 0\}$ be a martingale with respect to $\{Y_n\}$. Prove for any set of integers $k\leq l<m$ that

score 394 · Answer 1 · 2015-07-01 06:45:54

394

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Let $\{X_n; n\geq 0\}$ be a martingale with respect to $\{Y_n\}$. Prove for any set of integers $k\leq l<m$ that

Published on 01 Jul 2015 - 6:45

score 96 · Answer 2 · 2015-07-01 12:03:03

96

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If $(X_t,t\in I)$ is a process with values in $(E,\mathcal{E})$, are $\sigma(X_t,t\in I)$ and $\sigma(X)=X^{-1}(\mathcal{E}^{\otimes I})$ equal?

Published on 01 Jul 2015 - 12:03

score 3.5k · Answer 3 · 2026-04-09 08:31:47

3.5k

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Infinitesimal Generator of Poisson process

Published on 09 Apr 2026 - 8:31

score 102 · Answer 4 · 2015-07-01 23:39:28

102

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Variation processes and strong solutions of stochastic differential equations

Published on 01 Jul 2015 - 23:39

score 286 · Answer 5 · 2015-07-02 09:54:00

286

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Optional stopping/sampling for right-continuous supermartingales

Published on 02 Jul 2015 - 9:54

score 651 · Answer 6 · 2026-04-09 04:24:17

651

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If $(B_t)_{t\ge 0}$ is a Brownian motion and $\tau$ is a stopping time, then the stopped process $(B_{\min(\tau,t)})_{t\ge 0}$ is integrable

Published on 09 Apr 2026 - 4:24

score 3.4k · Answer 7 · 2026-04-09 02:27:52

3.4k

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Understanding Quadratic Variation

Published on 09 Apr 2026 - 2:27

score 6.5k · Answer 8 · 2026-04-09 07:33:00

6.5k

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Infinitesimal Generator of Ito Diffusion Process

Published on 09 Apr 2026 - 7:33

score 5.6k · Answer 9 · 2026-04-09 04:21:44

5.6k

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Prove that the increments of the Brownian motion are normally distributed

Published on 09 Apr 2026 - 4:21

score 6.9k · Answer 10 · 2026-04-09 04:20:45

6.9k

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(Elementary) Markov property of the Brownian motion

Published on 09 Apr 2026 - 4:20

score 82 · Answer 11 · 2026-04-02 01:51:32

82

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Proving technique used to show an equivalence to the definition of a Markov process

Published on 02 Apr 2026 - 1:51

score 247 · Answer 12 · 2026-04-02 17:42:51

247

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Motivation behind the definition of the Itô integral for elementary predictable processes

Published on 02 Apr 2026 - 17:42

score 324 · Answer 13 · 2026-04-09 04:24:17

324

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If $B$ is a BM and $\mathcal F_t=\sigma(B_s,s\le t)$, then $(B_{s+t}-B_t)_{s\ge 0}$ is independent of $\mathcal F_t^+:=\bigcap_{s>t}\mathcal F_s$

Published on 09 Apr 2026 - 4:24

score 1.6k · Answer 14 · 2015-07-05 20:46:22

1.6k

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Expected value of time integral of geometric brownian motion

Published on 05 Jul 2015 - 20:46

score 6.1k · Answer 15 · 2026-04-02 17:41:27

6.1k

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Fubini's Theorem for Stochastic Integral

Published on 02 Apr 2026 - 17:41

List Question

Let $\{X_n; n\geq 0\}$ be a martingale with respect to $\{Y_n\}$. Prove for any set of integers $k\leq l<m$ that

If $(X_t,t\in I)$ is a process with values in $(E,\mathcal{E})$, are $\sigma(X_t,t\in I)$ and $\sigma(X)=X^{-1}(\mathcal{E}^{\otimes I})$ equal?

Infinitesimal Generator of Poisson process

Variation processes and strong solutions of stochastic differential equations

Optional stopping/sampling for right-continuous supermartingales

If $(B_t)_{t\ge 0}$ is a Brownian motion and $\tau$ is a stopping time, then the stopped process $(B_{\min(\tau,t)})_{t\ge 0}$ is integrable

Understanding Quadratic Variation

Infinitesimal Generator of Ito Diffusion Process

Prove that the increments of the Brownian motion are normally distributed

(Elementary) Markov property of the Brownian motion

Proving technique used to show an equivalence to the definition of a Markov process

Motivation behind the definition of the Itô integral for elementary predictable processes

If $B$ is a BM and $\mathcal F_t=\sigma(B_s,s\le t)$, then $(B_{s+t}-B_t)_{s\ge 0}$ is independent of $\mathcal F_t^+:=\bigcap_{s>t}\mathcal F_s$

Expected value of time integral of geometric brownian motion

Fubini's Theorem for Stochastic Integral

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