Question

Evaluate $\mathbb{E}\left(\left[W\left(\frac{k}{n}\right)-W(t)\right]^2\right)$ for all $t\in\left(\frac{k}{n},\frac{k+1}{n}\right]$

score 41 · Answer 1 · 2026-04-09 10:18:24

41

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Evaluate $\mathbb{E}\left(\left[W\left(\frac{k}{n}\right)-W(t)\right]^2\right)$ for all $t\in\left(\frac{k}{n},\frac{k+1}{n}\right]$

Published on 09 Apr 2026 - 10:18

score 86 · Answer 2 · 2026-04-04 18:22:23

86

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Calculate $\mathbb{E}[M_{\alpha}^{p}(t)]$ for all $p>0$ and $t>0$, where $M_{\alpha}(t):=e^{\alpha W_t-\frac{\alpha^2}{2}t}$, $t\ge 0$

Published on 04 Apr 2026 - 18:22

score 700 · Answer 3 · 2026-04-09 10:16:51

700

Views

Application of Ito's isometry in deduction of Wiener Ito Chaos expansion

Published on 09 Apr 2026 - 10:16

score 369 · Answer 4 · 2015-08-07 17:26:06

369

Views

Novikov condition, martingale

Published on 07 Aug 2015 - 17:26

score 167 · Answer 5 · 2026-04-09 20:52:47

167

Views

Generator of a stochastic process

Published on 09 Apr 2026 - 20:52

score 2.5k · Answer 6 · 2026-04-11 02:29:14

2.5k

Views

Differentiating Stochastic Integral

Published on 11 Apr 2026 - 2:29

score 57 · Answer 7 · 2026-04-10 23:15:13

57

Views

Show that $X_n\in\mathcal{H}$, where $\mathcal{H}:=\{h(t):h(t)\text{ is an adapted process, }\mathbb{E}[\int_0^{\infty}h^2(t)dt]<\infty\}$

Published on 10 Apr 2026 - 23:15

score 363 · Answer 8 · 2026-04-02 19:34:45

363

Views

Burkholder's inequality for elementary stochastic integral

Published on 02 Apr 2026 - 19:34

score 103 · Answer 9 · 2026-04-04 18:22:24

103

Views

Show that $\mathbb{E}\left(\int_0^1X_n(t)dW(t)-\int_0^1X(t)dW(t)\right)^2\to 0$

Published on 04 Apr 2026 - 18:22

score 433 · Answer 10 · 2026-03-26 12:51:39

433

Views

Gradient descent method with random perturbation

Published on 26 Mar 2026 - 12:51

score 2.1k · Answer 11 · 2026-04-09 12:05:33

2.1k

Views

Calculation with Ito processes, what is $ds \, dt$, $dW_t \, ds$ and $dW_s \, dW_t$?

Published on 09 Apr 2026 - 12:05

score 132 · Answer 12 · 2026-04-04 22:00:58

132

Views

Doob Meyer decomposition for Super-martingales

Published on 04 Apr 2026 - 22:00

score 121 · Answer 13 · 2026-04-10 20:16:50

121

Views

interchanging spatial integral and time integral in the Brownian context

Published on 10 Apr 2026 - 20:16

score 45 · Answer 14 · 2026-03-29 07:28:58

45

Views

Show $Y(t)=X^{(1)}(t)-X^{(2)}(t)$ and $\lim_{t\to\infty} \mathbb{E}Y^2(t)=0$ , for $dX^{(i)}=\mu X^{(i)}dt+\sigma X^{(i)}dW$

Published on 29 Mar 2026 - 7:28

score 142 · Answer 15 · 2015-08-13 18:40:55

142

Views

Estimate mean and variance for a truncated sample set

Published on 13 Aug 2015 - 18:40

List Question

Evaluate $\mathbb{E}\left(\left[W\left(\frac{k}{n}\right)-W(t)\right]^2\right)$ for all $t\in\left(\frac{k}{n},\frac{k+1}{n}\right]$

Calculate $\mathbb{E}[M_{\alpha}^{p}(t)]$ for all $p>0$ and $t>0$, where $M_{\alpha}(t):=e^{\alpha W_t-\frac{\alpha^2}{2}t}$, $t\ge 0$

Application of Ito's isometry in deduction of Wiener Ito Chaos expansion

Novikov condition, martingale

Generator of a stochastic process

Differentiating Stochastic Integral

Show that $X_n\in\mathcal{H}$, where $\mathcal{H}:=\{h(t):h(t)\text{ is an adapted process, }\mathbb{E}[\int_0^{\infty}h^2(t)dt]<\infty\}$

Burkholder's inequality for elementary stochastic integral

Show that $\mathbb{E}\left(\int_0^1X_n(t)dW(t)-\int_0^1X(t)dW(t)\right)^2\to 0$

Gradient descent method with random perturbation

Calculation with Ito processes, what is $ds \, dt$, $dW_t \, ds$ and $dW_s \, dW_t$?

Doob Meyer decomposition for Super-martingales

interchanging spatial integral and time integral in the Brownian context

Show $Y(t)=X^{(1)}(t)-X^{(2)}(t)$ and $\lim_{t\to\infty} \mathbb{E}Y^2(t)=0$ , for $dX^{(i)}=\mu X^{(i)}dt+\sigma X^{(i)}dW$

Estimate mean and variance for a truncated sample set

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