Question

How can we show that the Dolean Dade exponential is a supermartingale without using the Ito's lemma

score 716 · Answer 1 · 2026-03-25 07:42:53

716

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How can we show that the Dolean Dade exponential is a supermartingale without using the Ito's lemma

Published on 25 Mar 2026 - 7:42

score 136 · Answer 2 · 2018-05-31 13:02:32

136

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Why do $\underset{t\leq u \leq T}{\max}W_u-W_t$ and $\underset{0\leq u \leq T-t}{\max}W_u-W_0$ have the same distribution?

Published on 31 May 2018 - 13:02

score 53 · Answer 3 · 2018-06-03 13:03:04

53

Views

Showing $B(s) - \frac{s}{t}B(t)$ is normal

Published on 03 Jun 2018 - 13:03

score 96 · Answer 4 · 2018-06-03 14:51:41

96

Views

$B(t)$ brownian motion, $[Y,Y](t)$ is qudratic variation,prove : 1. $[Y,Y](\infty)<\infty$ 2. for $\omega$ with $\int_0^\infty a(s)^2\, ds=\infty$,

Published on 03 Jun 2018 - 14:51

score 48 · Answer 5 · 2018-06-05 09:00:37

48

Views

Central limit theorem for "not the whole sum" in construction of Wiener measure.

Published on 05 Jun 2018 - 9:00

score 67 · Answer 6 · 2018-06-05 11:23:13

67

Views

Probability of hitting curve in the plane

Published on 05 Jun 2018 - 11:23

score 30 · Answer 7 · 2026-03-25 06:01:21

30

Views

Two different ways of expressing a stochastic integral?

Published on 25 Mar 2026 - 6:01

score 79 · Answer 8 · 2018-06-05 21:49:04

79

Views

$E|B_t - B_s|^4 = 3|t-s|^2$

Published on 05 Jun 2018 - 21:49

score 30 · Answer 9 · 2026-03-25 03:20:23

30

Views

Hitting time of upper boundary given that process has not touched lower boundary

Published on 25 Mar 2026 - 3:20

score 20 · Answer 10 · 2018-06-06 16:00:41

20

Views

Characterization of standard multidimensional BM as independent linear BMs

Published on 06 Jun 2018 - 16:00

score 651 · Answer 11 · 2026-03-24 22:12:44

651

Views

Show that this stochastic process is a.s. strictly positive.

Published on 24 Mar 2026 - 22:12

score 79 · Answer 12 · 2018-06-07 09:49:08

79

Views

A question about the exsistence of Brownian Motion?

Published on 07 Jun 2018 - 9:49

score 2.1k · Answer 13 · 2018-06-08 15:58:11

2.1k

Views

Expectation of exponential of a sum of two Wiener processes

Published on 08 Jun 2018 - 15:58

score 183 · Answer 14 · 2018-06-11 06:23:00

183

Views

Expected value of Brownian motion when it is less that a given number:$E[W_t\mathbb{1}_{(W_t \leq a)}] $

Published on 11 Jun 2018 - 6:23

score 38 · Answer 15 · 2026-03-25 06:03:46

38

Views

Can this function: $\int_0^t({B_s}^2+s)^2$ $ds$ be simplified any further using Ito's Lemma or other methods?

Published on 25 Mar 2026 - 6:03

List Question

How can we show that the Dolean Dade exponential is a supermartingale without using the Ito's lemma

Why do $\underset{t\leq u \leq T}{\max}W_u-W_t$ and $\underset{0\leq u \leq T-t}{\max}W_u-W_0$ have the same distribution?

Showing $B(s) - \frac{s}{t}B(t)$ is normal

$B(t)$ brownian motion, $[Y,Y](t)$ is qudratic variation,prove : 1. $[Y,Y](\infty)<\infty$ 2. for $\omega$ with $\int_0^\infty a(s)^2\, ds=\infty$,

Central limit theorem for "not the whole sum" in construction of Wiener measure.

Probability of hitting curve in the plane

Two different ways of expressing a stochastic integral?

$E|B_t - B_s|^4 = 3|t-s|^2$

Hitting time of upper boundary given that process has not touched lower boundary

Characterization of standard multidimensional BM as independent linear BMs

Show that this stochastic process is a.s. strictly positive.

A question about the exsistence of Brownian Motion?

Expectation of exponential of a sum of two Wiener processes

Expected value of Brownian motion when it is less that a given number:$E[W_t\mathbb{1}_{(W_t \leq a)}] $

Can this function: $\int_0^t({B_s}^2+s)^2$ $ds$ be simplified any further using Ito's Lemma or other methods?

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