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probability transition function
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(Definition)
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A probability transition function (p.t.f., or just t.f. in context) on a measurable space
 is a family  ,
 of transition probabilities on
 such that for every three real numbers  , the family satisfies the Chapman-Kolmogorov equation
for every
 and
 . The t.f. is said to be homogeneous if  depends on  and  only through their difference  . In this case, we write
 and the family
 is a semigroup, and the Chapman-Kolmogorov equation reads
- 1
- D. Revuz & M. Yor, Continuous Martingales and Brownian Motion, Third Edition Corrected. Volume 293, Grundlehren der mathematischen Wissenschaften. Springer, Berlin, 2005.
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"probability transition function" is owned by mcarlisle.
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| Also defines: |
probability transition function, homogeneous probability transition function, Chapman-Kolmogorov equation |
| Keywords: |
random stochastic process transition function semigroup probability |
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Cross-references: semigroup, real numbers, transition probabilities, measurable space
There is 1 reference to this entry.
This is version 5 of probability transition function, born on 2006-09-01, modified 2006-09-02.
Object id is 8306, canonical name is ProbabilityTransitionFunction.
Accessed 2066 times total.
Classification:
| AMS MSC: | 60J35 (Probability theory and stochastic processes :: Markov processes :: Transition functions, generators and resolvents) |
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Pending Errata and Addenda
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