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edited Aug 4 at 19:56

I am trying to show the following statement

Let $D\subset \mathbb{R}^2$ be an open and bounded subset. $\Pi=(P^x : x \in D )$ a Family of standard Brownian Motions started at $x \in D$. Then $\Pi$ ist a tight (or relativly compact due to Prorhorvs Theorem).

I need that result to proof the existence of a certain type of process on the Sierpinski CarpetProcess. Unfortunately I do not have any experience working with the concept of "tightness". Perhaps Arzelà-Ascoli would work but I have no idea how to apply it.

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edited Aug 4 at 17:59

Anton Geraschenko♦♦
13.7k●3●48●108

Hallo together

Thanks very much

I am trying to show the following statement

Let $D\subset \mathbb{R}^2$ be an open and bounded subset. $\Pi=(P^x : x \in advanceD )$ a Family of standard Brownian Motions started at $x \in D$. Then $\Pi$ ist a tight (or relativly compact due to Prorhorvs Theorem).

I need that result to proof the existence of a certain type of process on the Sierpinski Carpet. Unfortunately I do not have any experience working with the concept of "tightness". Perhaps Arzelà-Ascoli would work but I have no idea how to apply it.

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edited Aug 4 at 17:17

Boldwing
100●9

Tightness / relativ compactness of a Family of Brownian Motions

Hallo together

I am trying to show the following statement

Let $D\subset \mathbb{R}^2$ be an open and bounded subset. $\Pi=(P^x : x \in D )$ a Family of standard Brownian Motions started at $x \in D$. Then $\Pi$ ist a tight (or relativly compact due to Prorhorvs Theorem).