Mesures Associees Aux Fonctionnelles Additives de Markov. I

Revuz, Daniel

doi:10.2307/1995386

Cited by 61 publications

(81 citation statements)

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“…Exactly as in [9] one establishes the following proposition. Proposition 7.4 is relatively elementary and is valid under the assumption that ^ is an excessive reference measure for X.…”

Section: Jomentioning

confidence: 75%

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Multiplicative functionals of dual processes

Getoor¹

1971

Annales De L’institut Fourier

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“…Exactly as in [9] one establishes the following proposition. Proposition 7.4 is relatively elementary and is valid under the assumption that ^ is an excessive reference measure for X.…”

Section: Jomentioning

confidence: 75%

“…The ideas and tech-niques of this section are due to Revuz [9]. We merely adapt his methods to cover the situation which interests us here.…”

Section: Measures Associated With Multiplicative Functionalsmentioning

confidence: 99%

Multiplicative functionals of dual processes

Getoor¹

1971

Annales De L’institut Fourier

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“…It is known (see [22,30]) that under (4.8), the family of all integrable positive AFs of X and the family of all bounded positive soft measures on R + × D are in one-to-one correspondence. In what follows the additive functional corresponding to a positive bounded soft measure μ will be denoted by A μ .…”

Section: Additive Functionals and Soft Measuresmentioning

confidence: 99%

Existence and large-time asymptotics for solutions of semilinear parabolic systems with measure data

Klimsiak

2014

J. Evol. Equ.

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Abstract. We study the Cauchy-Dirichlet problem for monotone semilinear uniformly elliptic second-order parabolic systems in divergence form with measure data. We show that under mild integrability conditions on the data, there exists a unique probabilistic solution of the system. We also show that if the operator and the data do not depend on time, then the solution of the parabolic system converges as t → ∞ to the solution of the Dirichlet problem for an associated elliptic system. In fact, we prove some results on the rate of the convergence.

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“…Therefore it follows from [12] that for any Radon measure # in Ka, there exists a unique positive continuous additive functional A = (At)t> 0 of X such that…”

Section: If a Radon Measure It Is In Ka Then It Does Not Charge Polamentioning

confidence: 99%

The gauge theorem for a class of additive functionals of zero energy

Glover

Rao

Song

1994

Probab. Th. Rel. Fields

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Summary.In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form f ~o q(Bs)ds, where q is a function in the Kato class.Subsequently, the theorem was extended to additive functionals with Revuz measures/t in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded variation. These additive functionals may not be semi-martingales, but correspond to a collection of distributions that belong to the Kato class in a suitable sense. Our gauge theorem generalizes the earlier versions of the gauge theorem. Mathematics Subject Classification (1991): 60J65, 60J55, 60J57Brownian motion has long been used to treat the Dirichlet problem and other differential equations involving the Laplacian in a probabilistic manner. In resolving the Dirichlet problem, one tries to solve Au = 0 on some bounded open domain D subject to the condition u = f on the boundary of D, for some specified function f Kac showed that the probabilistic approach can be extended to treat differential operators of the form A -q, or more generally, of the form A -# by considering Brownian motion "killed" by a multiplicative functional associated with q or #.

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Mesures Associees Aux Fonctionnelles Additives de Markov. I

Cited by 61 publications

References 0 publications

Multiplicative functionals of dual processes

Multiplicative functionals of dual processes

Existence and large-time asymptotics for solutions of semilinear parabolic systems with measure data

The gauge theorem for a class of additive functionals of zero energy

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