Question

$E e^{B_s^2 e^{2B_s}}\mathbb{1}_{\{B_s\leq -1\}} < \infty$

score 47 · Answer 1 · 2026-04-15 03:03:39

47

Views

$E e^{B_s^2 e^{2B_s}}\mathbb{1}_{\{B_s\leq -1\}} < \infty$

Published on 15 Apr 2026 - 3:03

score 88 · Answer 2 · 2026-04-16 19:10:46

88

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Show that $Z_t = \sqrt{\sqrt{2t}e^{-\sqrt{2t}}} B_{e^{\sqrt{2t}}-1}$ solves $dZ_t = f(t)Z_tdt +dM_t$ and find $f(t)$.

Published on 16 Apr 2026 - 19:10

score 344 · Answer 3 · 2026-04-16 04:47:12

344

Views

Compute $E(2B_T e^{-B_T}+ 4e^{-B_T})$ for $B = (B_t)_{t \geq 0}$ a standard Brownian motion and $T=\inf\{t \geq 0 : |B_t|=1\}$.

Published on 16 Apr 2026 - 4:47

score 266 · Answer 4 · 2026-04-16 00:11:40

266

Views

Evaluate $E[B(u)B(u+v)B(u+v+w)B(u+v+w+x)] $, where $\{B(t); t\ge 0\}$ is a standard Brownian Motion

Published on 16 Apr 2026 - 0:11

score 80 · Answer 5 · 2026-04-14 00:35:21

80

Views

Using Novikov Theorem to Derive Fokker-Planck/ Smoluchowksi Equation

Published on 14 Apr 2026 - 0:35

score 235 · Answer 6 · 2026-04-12 10:02:32

235

Views

Proving Integration by Parts for Brownian Motion and function of bounded variation

Published on 12 Apr 2026 - 10:02

score 160 · Answer 7 · 2026-04-16 11:36:06

160

Views

Show that $Y_t \int_0^t \frac{1}{Y_s} ds$ and $\int_0^t Y_s ds$ are equal in distribution

Published on 16 Apr 2026 - 11:36

score 219 · Answer 8 · 2026-04-13 18:44:10

219

Views

Wiener Process. Where can I find proof.

Published on 13 Apr 2026 - 18:44

score 112 · Answer 9 · 2026-04-13 17:39:19

112

Views

What's the time derivative of this characteristic function?

Published on 13 Apr 2026 - 17:39

score 55 · Answer 10 · 2026-04-14 12:40:12

55

Views

Why $|W_t|-L_t$ is a Brownian motion

Published on 14 Apr 2026 - 12:40

score 98 · Answer 11 · 2026-04-13 05:36:48

98

Views

Show that stopping time of a Brownian Motion is independent of the particular BM

Published on 13 Apr 2026 - 5:36

score 592 · Answer 12 · 2026-04-11 20:30:22

592

Views

Is a sum of Brownian motions a Gaussian process?

Published on 11 Apr 2026 - 20:30

score 149 · Answer 13 · 2026-04-12 03:02:06

149

Views

Brownian motion exercise

Published on 12 Apr 2026 - 3:02

score 205 · Answer 14 · 2026-04-12 13:32:44

205

Views

Is this process a Brownian motion?

Published on 12 Apr 2026 - 13:32

score 235 · Answer 15 · 2026-04-14 11:30:36

235

Views

Modulus of continuity of Brownian Motion, independent of particular choice of Brownian Motion

Published on 14 Apr 2026 - 11:30

List Question

$E e^{B_s^2 e^{2B_s}}\mathbb{1}_{\{B_s\leq -1\}} < \infty$

Show that $Z_t = \sqrt{\sqrt{2t}e^{-\sqrt{2t}}} B_{e^{\sqrt{2t}}-1}$ solves $dZ_t = f(t)Z_tdt +dM_t$ and find $f(t)$.

Compute $E(2B_T e^{-B_T}+ 4e^{-B_T})$ for $B = (B_t)_{t \geq 0}$ a standard Brownian motion and $T=\inf\{t \geq 0 : |B_t|=1\}$.

Evaluate $E[B(u)B(u+v)B(u+v+w)B(u+v+w+x)] $, where $\{B(t); t\ge 0\}$ is a standard Brownian Motion

Using Novikov Theorem to Derive Fokker-Planck/ Smoluchowksi Equation

Proving Integration by Parts for Brownian Motion and function of bounded variation

Show that $Y_t \int_0^t \frac{1}{Y_s} ds$ and $\int_0^t Y_s ds$ are equal in distribution

Wiener Process. Where can I find proof.

What's the time derivative of this characteristic function?

Why $|W_t|-L_t$ is a Brownian motion

Show that stopping time of a Brownian Motion is independent of the particular BM

Is a sum of Brownian motions a Gaussian process?

Brownian motion exercise

Is this process a Brownian motion?

Modulus of continuity of Brownian Motion, independent of particular choice of Brownian Motion

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