The Blumenthal-Getoor-McKean Theorem Revisited

Fitzsimmons, P. J.; Getoor, R. K.; Sharpe, M. J.

doi:10.1007/978-1-4612-3458-6_4

Cited by 9 publications

(2 citation statements)

References 15 publications

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“…Suppose that U is the resolvent of a Borel right process. Then: a) From the above equivalence i) ⇐⇒ ii) and Proposition 2.5 in [17] it follows that s ∈ E U , s < ∞, will be ξ -regular if and only if there exists a continuous additive functional whose associated potential is equal s ξ-q.e. b) The assertions iii) and iv) in Proposition 2.2 are versions of the characterization of the regularity in terms of hitting times (see (3.4) in [20]) instead of arbitrary stopping times.…”

Section: Iii) For Every Increasing Sequencementioning

confidence: 99%

Excessive kernels and Revuz measures

Beznea¹,

Boboc

2000

Probab Theory Relat Fields

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We consider a proper submarkovian resolvent of kernels on a Lusin measurable space and a given excessive measure ξ . With every quasi bounded excessive function we associate an excessive kernel and the corresponding Revuz measure. Every finite measure charging no ξ -polar set is such a Revuz measure, provided the hypothesis (B) of Hunt holds. Under a weak duality hypothesis, we prove the Revuz formula and characterize the quasi boundedness and the regularity in terms of Revuz measures. We improve results of Azéma [2] and Getoor and Sharpe [20] for the natural additive functionals of a Borel right process.

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Section: Iii) For Every Increasing Sequencementioning

confidence: 99%

Excessive kernels and Revuz measures

Beznea¹,

Boboc

2000

Probab Theory Relat Fields

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“…The celebrated Blumenthal-Getoor-McKean Theorem (see Chap V in [4], and also [9] for a modern approach) states that two Markov processes X and Y with the same hitting distributions are related by time-change: there exists some continuous strictly increasing additive functional of X such that if T is its right-continuous inverse, then Y and X • T are equivalent processes. Intuitively, this means that X and Y have the same sample paths, but that they live on them with different "speeds".…”

Section: Introductionmentioning

confidence: 99%

Subordination in the wide sense for Lévy processes

Simon

1999

Probab Theory Relat Fields

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Given (µ t ) t ≥ 0 a transient convolution semigroup over R d , we characterize the transient semi-groups which are subordinate in the wide sense to the latter, via some quotient relation between the two Lévy generators. This is also equivalent to an inclusion between excessive cones. Thanks to a theorem of Hirsch, this allows us in big dimensions to give a probabilistic description of some measures satisfying the classical maximum principle. Mathematics Subject Classification (1991): 60J30, 60J45

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Semidynamical Systems with the Same Order Relation

Rhouma

Bezzarga

2004

Proceedings of the International Conference on Stochastic Analysis and Applications

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The Blumenthal-Getoor-McKean Theorem Revisited

Cited by 9 publications

References 15 publications

Excessive kernels and Revuz measures

Excessive kernels and Revuz measures

Subordination in the wide sense for Lévy processes

Semidynamical Systems with the Same Order Relation

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