Kybernetika 62 no. 1, 7-17, 2026

A note on measurable modifications

Martin Ondreját and Jan SeidlerDOI: 10.14736/kyb-2026-1-0007

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.

Keywords:

stochastic processes, measurable modification

Classification:

60G05

paper.pdf

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