Feller process

Let E be a LCCB space (locally compact with a countable base; usually a subset of n for some n) and C0(E)=C0(E,) be the space of continuous functionsMathworldPlanetmath on E that vanish at infinity. (We may write C0 as shorthand.) A Feller semigroup on C0(E) is a family of positivePlanetmathPlanetmath linear operators Tt,t0, on C0(E) such that

  • T0=Id and ||Tt||1 for every tT, i.e. {Tt}tT is a family of contracting maps;

  • Tt+s=TtTs (the semigroup property);

  • limt0||Ttf-f||=0 for every fC0(E).

A probability transition function associated with a Feller semigroup is called a Feller transition function. A Markov process having a Feller transition function is called a Feller process.


Title Feller process
Canonical name FellerProcess
Date of creation 2013-03-22 16:12:40
Last modified on 2013-03-22 16:12:40
Owner mcarlisle (7591)
Last modified by mcarlisle (7591)
Numerical id 6
Author mcarlisle (7591)
Entry type Definition
Classification msc 60J35
Defines Feller semigroup
Defines Feller transition function
Defines Feller process
Defines LCCB