LAWS OF EXCURSIONS ASSOCIATED TO ADDITIVE FUNCTIONALS

Auteurs-es

  • H BOUTABIA Universté Badji-Mokhtar Annaba 23000, B.P.12.

Mots-clés :

Standard process, Predictable process, Excursion, Additive functional, Conditional law, Exit measure, Kuznetsov process.

Résumé

Let (Pt) be a right borel semigroup and let (St) the right inverse of a continuous additive functional (Bt). Let ( )
t R t Y

be a
right stationary process with random birth and death, Markov with semi group (Pt) under the Kuznetsov measure Q
associated to an excessive measure. We define, under the assumption that the characteristic measure
{ } ( ) 1
B 0 Yt υ Q I B dt ∈. = ∫ of (Bt) is purely excessive for the semigroup (Ps), an additive functional for ( )
t R t Y

in terms of
(Bt) and we study the laws of excursions associated to the regenerative set which consists in times of discontinuity of the
right inverse (Ut) of this additive functional. More precisely, if we note by ( ) t Φ the process
Ut Y ⎛ ⎞
⎜ ⎟
⎜ ⎟
⎝ ⎠
and by H the σ -
algebra generated by Ht (t∈R) where Ht is the Q-completion of 0
t H + ( 0
t ⎛H ⎞
⎜ ⎟
⎝ ⎠ is the natural filtration of ( ) t Φ ),
then if T is a ( ) t H -stopping time such that T T U U − ≠ and T − T Φ ≠ Φ , the conditional law of the excursion
straddling T T U U −
⎤ ⎡
⎥⎦ ⎢⎣ , with respect to H depend only on T Φ and T − Φ . Conditional laws of pairs of excursions
are also considered.

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Biographie de l'auteur-e

H BOUTABIA, Universté Badji-Mokhtar Annaba 23000, B.P.12.

Département de
Mathématiques, Faculté
des Sciences

Références

- BOUTABIA H..-Lois conditionnelles des excursions

d’un processus de Markov à naissance et mort aléatoires,

Portugaliae Mathematica., Vol 56 fasc 2, 239-255, 1999.

- BOUTABIA H.-Additive functionals and excursions of

Kuznetsov processes, International Journal of Mathematics

and Mathematical Sciences., 2031-2040 (2005).

- GETOOR R.K.and SHARPE M.J.-Two results on dual

excursions, Seminar on Stochastic Processes1981,

Birkauser (1981), 31-52.

- GETOOR R.K.-Killing a Markov process under a

stationary measure involves creation, Ann.Prob.,16(1988).

- JACODS.PA-Excursions of a Markov process induced

by continuous additive functionals, Z.Wahrs.Verw.Geb.

(1978),325-336.

- KASPI H.-Excursion laws of Markov processes in

classical duality, Ann.Prob., 33, (1985), 492-518.

- KASPI H.-Random time changes for processes with

random birth and death, Ann.Prob., 16, (1988), 586-599

- KUZNETSOV S.E.-Construction of Markov processes

with random times of birth and death, Prob.Th. Fiel 18

(1973), 571-575.

-MAISONNEUVE B.-Systéme de sortie

Dt F ⎛ ⎞

⎜ ⎟

⎜ ⎟

⎝ ⎠

-

prévisibles, Prob.Th.Fields 80 (1989), 395-405.

- MITRO J.B.-Exit Systems for Dual Markov

Processes, Z.Wahrs.Verw

Geb. 66(1984), 259-267.

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Publié-e

2006-12-01

Comment citer

BOUTABIA, H. (2006). LAWS OF EXCURSIONS ASSOCIATED TO ADDITIVE FUNCTIONALS. Sciences & Technologie. A, Sciences Exactes, (24), 41–45. Consulté à l’adresse https://revue.umc.edu.dz/a/article/view/151

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