probability transition function

A probability transition function (p.t.f., or just t.f. in context) on a measurable spaceMathworldPlanetmathPlanetmath (Ω,) is a family Ps,t, 0s<t of transition probabilities on (Ω,) such that for every three real numbers s<t<v, the family the Chapman-Kolmogorov equation


for every xΩ and A. The t.f. is said to be if Ps,t depends on s and t only through their t-s. In this case, we write Pt,0=Pt and the family {Pt,t0} is a semigroup, and the Chapman-Kolmogorov equation reads



Title probability transition function
Canonical name ProbabilityTransitionFunction
Date of creation 2013-03-22 16:12:37
Last modified on 2013-03-22 16:12:37
Owner mcarlisle (7591)
Last modified by mcarlisle (7591)
Numerical id 8
Author mcarlisle (7591)
Entry type Definition
Classification msc 60J35
Defines probability transition function
Defines homogeneous probability transition function
Defines Chapman-Kolmogorov equation