modification of a stochastic process

Let ${\{X_t\}}_{t\ge 0}$, ${\{Y_t\}}_{t\ge 0}$ be stochastic processes on $(\mathrm{\Omega },ℱ,P)$. ${\{X_t\}}_{t\ge 0}$ is a modification of ${\{Y_t\}}_{t\ge 0}$ if

$$P[\{\omega :X_t(\omega )=Y_t(\omega )\}]=1$$

for all $t\in [0,\mathrm{\infty }).$

Title	modification of a stochastic process
Canonical name	ModificationOfAStochasticProcess
Date of creation	2013-03-22 16:09:44
Last modified on	2013-03-22 16:09:44
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	9
Author	georgiosl (7242)
Entry type	Definition
Classification	msc 60G07
Classification	msc 60G05
Related topic	DistributionsOfAStochasticProcess
Defines	modification