Question

$ \sup_{t \geq 0}\big( |B_t|-t^{r/2}\big) \text{ and } \sup_{t \geq 0}\big( \frac{|B_t|}{1+t^{r/2}}\big)^\rho$ have the same law?

score 32 · Answer 1 · 2026-04-05 11:05:05

32

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$ \sup_{t \geq 0}\big( |B_t|-t^{r/2}\big) \text{ and } \sup_{t \geq 0}\big( \frac{|B_t|}{1+t^{r/2}}\big)^\rho$ have the same law?

Published on 05 Apr 2026 - 11:05

score 1.8k · Answer 2 · 2015-10-12 12:44:41

1.8k

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score 1.2k · Answer 14 · 2015-10-24 11:17:39

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score 57 · Answer 15 · 2015-10-25 12:48:29

57

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List Question

$ \sup_{t \geq 0}\big( |B_t|-t^{r/2}\big) \text{ and } \sup_{t \geq 0}\big( \frac{|B_t|}{1+t^{r/2}}\big)^\rho$ have the same law?

The expected value of stop-time for Brownian motion $\tau=\min_t\{B_t^2\geq t+1\}$.

SLE theory, showing that $T_u$ is a.s. finite

Proof of a stochastic process being a martingale

AR(1) process: Finding the distribution of the prediction error

Brownian motion : disjoint intervals with the same maximum

brownian motion conditioned on past and future observation

Almost surely, for all $s \ge 0$, there exist $t$, $u \ge s$ with $B_t < 0 < B_u$?

Proof that the stopping time for a Brownian Motion is finite for given target levels

Correspondence between multi-dimensional Brownian motion and harmonic functions

Lebesgue Thorn and Brownian motion

$2$ d Brownian motion move from one point to another

Extension of Dynkin's formula, conclude that process is a martingale.

Prove that the first hitting time $\tau_x:=\inf\left\{t\ge 0:B_t=x\right\}$ of a Brownian motion is almost surely finite

Distribution of a Brownian bridge

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