imported>Jlwoodwa: tag as one source

2024-03-13T03:28:27Z

tag as one source

New page

{{one source |date=March 2024}}
An '''increasing process''' is a [[stochastic process]]...

:<math>(X_t)_{t \in M}</math>

...where the [[random variable]]s <math>X_t</math> which make up the process are increasing [[almost surely]] and [[adapted process|adapted]]:

:<math>0=X_0 \leq X_{t_1} \leq \cdots . </math>

A '''continuous increasing process''' is such a process where the set <math>M</math> is continuous.

Consider a stochastic process <math>(\Chi_t)</math> satisfying <math>X_t \leq X_s</math> a.s. for all <math>t \leq s</math> My question is: Does there exist a modification <math>\breve{X}</math> of ,<math>X</math> which almost surely has increasing sample paths <math>t \mapsto \breve{X}_t(\omega)</math>?<ref>{{Cite web |title=Increasing stochastic process |url=https://mathoverflow.net/questions/168757/increasing-stochastic-process |access-date=2023-05-06 |website=MathOverflow |language=en}}</ref>

==References==
{{reflist}}

[[Category:Stochastic processes]]

{{probability-stub}}

Increasing process - Revision history

imported>Jlwoodwa: tag as one source