Question

Using Feynman-Kac, compute the following:

score 420 · Answer 1 · 2015-07-28 20:14:27

420

Views

Using Feynman-Kac, compute the following:

Published on 28 Jul 2015 - 20:14

score 361 · Answer 2 · 2015-07-29 17:18:17

361

Views

Brownian motion: Strong Markov versus translation invariance

Published on 29 Jul 2015 - 17:18

score 248 · Answer 3 · 2026-03-29 16:58:02

248

Views

Rewriting probabilities as expectation

Published on 29 Mar 2026 - 16:58

score 478 · Answer 4 · 2026-04-03 02:16:02

478

Views

Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion

Published on 03 Apr 2026 - 2:16

score 99 · Answer 5 · 2015-07-30 18:10:30

99

Views

Show that $\mathbb{P}(\tau_{0}>T)\approx\frac{1}{\sqrt{T}}$ where $\{ B(t) : t\geq 0\}$ is a linear brownian motion started at $B(0)=1$

Published on 30 Jul 2015 - 18:10

score 701 · Answer 6 · 2026-03-29 05:35:14

701

Views

Trying to understand Tanaka's example of SDE.

Published on 29 Mar 2026 - 5:35

score 90 · Answer 7 · 2015-08-02 23:57:41

90

Views

Continuity of the Loewner flow (SLE theory).

Published on 02 Aug 2015 - 23:57

score 351 · Answer 8 · 2026-03-29 07:28:57

351

Views

Find $\mathbb{E}_{X_0 = x} X_\tau$ for an Ornstein-Uhlenbeck process $(X_t)_{t \geq 0}$ where $\tau = \inf\{t>0 \mid X_t \notin [a,b]\}$

Published on 29 Mar 2026 - 7:28

score 40 · Answer 9 · 2015-08-05 18:24:41

40

Views

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 05 Aug 2015 - 18:24

score 699 · Answer 10 · 2026-02-23 03:00:02

699

Views

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

Published on 23 Feb 2026 - 3:00

score 90 · Answer 11 · 2026-03-29 07:28:57

90

Views

Compute $\mathbb{E}[\tilde{X}_t]$, where $\tilde{X}_t=X_t=(1-t)\int_0^t\frac{1}{1-s}dW_s$ for $0\le t<1$ and $\tilde{X}_t=0$ for $t=1$

Published on 29 Mar 2026 - 7:28

score 113 · Answer 12 · 2015-08-07 16:40:38

113

Views

Process convergence of sum of i.i.d. random variables

Published on 07 Aug 2015 - 16:40

score 55 · Answer 13 · 2015-08-09 16:35:53

55

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 09 Aug 2015 - 16:35

score 3.6k · Answer 14 · 2026-04-02 03:36:46

3.6k

Views

Joint distribution of Brownian motion and its running maximum

Published on 02 Apr 2026 - 3:36

score 45 · Answer 15 · 2026-03-29 07:29:02

45

Views

Calculate the distance $d_{\mathcal{H}}(X_n,X):=\mathbb{E}\left(\int_0^{\infty}(X_n(t)-X(t))^2dt\right)$ for all $n\ge 1$

Published on 29 Mar 2026 - 7:29

List Question

Using Feynman-Kac, compute the following:

Brownian motion: Strong Markov versus translation invariance

Rewriting probabilities as expectation

Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion

Show that $\mathbb{P}(\tau_{0}>T)\approx\frac{1}{\sqrt{T}}$ where $\{ B(t) : t\geq 0\}$ is a linear brownian motion started at $B(0)=1$

Trying to understand Tanaka's example of SDE.

Continuity of the Loewner flow (SLE theory).

Find $\mathbb{E}_{X_0 = x} X_\tau$ for an Ornstein-Uhlenbeck process $(X_t)_{t \geq 0}$ where $\tau = \inf\{t>0 \mid X_t \notin [a,b]\}$

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

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

Compute $\mathbb{E}[\tilde{X}_t]$, where $\tilde{X}_t=X_t=(1-t)\int_0^t\frac{1}{1-s}dW_s$ for $0\le t<1$ and $\tilde{X}_t=0$ for $t=1$

Process convergence of sum of i.i.d. random variables

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

Joint distribution of Brownian motion and its running maximum

Calculate the distance $d_{\mathcal{H}}(X_n,X):=\mathbb{E}\left(\int_0^{\infty}(X_n(t)-X(t))^2dt\right)$ for all $n\ge 1$

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