Processus de Markov by Paul-André Meyer (auth.)

By Paul-André Meyer (auth.)

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Sample text

T ; sont ra- . - 57 - g' o Xt_ < g oXt. ~ g"o Xt. (g'o Xt) et l ' 4 g a l i t 6 fonction extremes La relation ( 3 2 . 1) a y a n t mesurables par uniforme convergence COROLLAIRE • . - Soit f la limite sellement d'4tablir ( 3 2 . 1) p o u r la pour elle s'4tend les potentiels ~ tousles de fonctions 414ments de U . une fonction p-excessive d'une suite mesurables et o n o b t i e n t croissante born6es (33. l) si l ' o n a p. s. - Soit , pour (34. a p o u r poserons fune presque fonction (e " p t f o X t ) , a u s e n s de l e c a s o~ .

CONTINUITE A DROITE DES TRIBUS . Le theoreme suivant est d'habitude enonce en m~me temps print4 de Markov forte ; nous l'en s4parons pour des raisons de clart4 THEOREME . -Soit port ~ une famille (X t) un processus continu ~ que la pro. droite, m a r k o v i e n . E' . La martingale martingale Soient ~ la famille sE[0,t[ et tout fA f~ Xt dP L'extension imrn4diate a u c a s off f ait s>t f) d ~ mesurable) est ~quivaut ~ l'~nonc4 . - markovien, le processus (F~ e_t (=F# s o n t c o n t i n u e s .

I1 e s t 6 v i d e n t q u e l e s n o y a u x de convolution, ~:i~les v Soit sante = g par un chapeau scalaire dans sont des noyaux e ' P t T r t dt (__Ft) d e t r i b u s , a d m e t t a n t produit de la r4solvante mesures (X t) un p r o c e s s u s , Nous noterons s le tels que ; on a E[exp(i)[Fs] = exp(-i) [ i t - s ( X s ' e x p ( i < u , .

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