A note on measurable modifications
Abstract
We present, with purely didactic aims, a simple and essentially self-contained proof of two necessary and sufficient conditions for existence of a measurable modification of a stochastic process with values in a separable complete metric space.Existence of a measurable modification of a stochastic process continuous in probability is an immediate consequence.
Fields of Study & Subjects
Probability and Statistical Research
Advanced Banach Space Theory
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Kybernetika
- Pages
- 7–17
- Publication date
- 13 January 2026
- Language
- EN