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Feller process (Definition)

Let $ E$ be a LCCB space (locally compact with a countable base; usually a subset of $ \mathbb{R}^n$ for some $ n \in \mathbb{N}$) and $ C_0(E) = C_0(E, \mathbb{R})$ be the space of continuous functions on $ E$ that vanish at infinity. (We may write $ C_0$ as shorthand.) A Feller semigroup on $ C_0(E)$ is a family of positive linear operators $ T_t, t \geq 0$, on $ C_0(E)$ such that

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.

Bibliography

1
D. Revuz & M. Yor, Continuous Martingales and Brownian Motion, Third Edition Corrected. Volume 293, Grundlehren der mathematischen Wissenschaften. Springer, Berlin, 2005.



"Feller process" is owned by mcarlisle.
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Also defines:  Feller semigroup, Feller transition function, Feller process, LCCB
Keywords:  Feller Markov random stochastic process semigroup
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Cross-references: probability transition function, property, semigroup, maps, linear operators, positive, vanish at infinity, continuous functions, subset, base, countable, locally compact
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This is version 3 of Feller process, born on 2006-09-01, modified 2006-09-01.
Object id is 8307, canonical name is FellerProcess.
Accessed 2776 times total.

Classification:
AMS MSC60J35 (Probability theory and stochastic processes :: Markov processes :: Transition functions, generators and resolvents)

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