Semi-martingales sur des varietes, et martingales conformes by L. Schwartz

By L. Schwartz

Ebook by means of Schwartz, L.

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Extra info for Semi-martingales sur des varietes, et martingales conformes sur des varietes analytiques complexes (Lecture Notes in Mathematics) (French Edition)

Sample text

Mi , M i > + ; M j , M . > + 2 ) . 3 3 On d i r a qu'un couple de p r o c e s s u s ~ d a n s F~ e s t conforme, E~F= c'est E×F, M, N~ e t soit NM p a r N sont q u e e s t un p r o c e s s u s lement conforme, bornbs, le et de E e t un c o u p l e dit conforme. conforme forme. Alors fonctions si les le Plus E = F, eonforme, s_i_i f e_~_t g s o n t de ~ c o n s t i t u e n t encore holomorphes nombre fini q u e M+N si E= ¢). et seulement Si E= tN si ses conforme. optionnels loca- car des applications vectoriels, par conforme, quelconque conformes~ e n t r a l n*e holo- ( f o M,g o N) e s t quelconques d'int~grales bornbes un ensemble que un e n s e m b l e ~ de m a r t i n g a l e s lin~aires localement cela des processus de d e u x m a r t i n g a l e s combinaisons ~ dire d e u x ~ d e u x un c o u p l e espaces dans et darts E s i H, K s o n t d'autres bquivaut ~quivalent ~ valeurs gbn~ralement, couple optionnelles d'un Si c'est Alors, ~ valeurs des martingales cou_~_~ (H • M,K ° N) e s t de F d a n s Cela conformes, forment si = HK • = 0.

Y' Soit u n Y'n ~ - a n a l y t i q u e m e n t existe, martingale (resp. un recouvrement 2) lieu conforme. d'abord de p r e n d r e fonction £ ~n s u r sur partie il X une semi-martingale Y~ p l u r i h a r m o n i q u e Dbmontrons suffit une une martingale sur sont et martingale I1 existe Alors AAX-I(V"), n nue sur 1) d a n s Y~, ~ s o i t (il A a une continue) : une boule). avec C2 s u r ~l~mentaire. fn = ~ + i~n C2, sur Anx-t(¥'), D~monstration tr~s conforme~ - Th6or6me VIII de c l a s s e est de c e p a r a g r a p h e eonforme.

2) Soit vement X une continue revStement 6quivalente sur A a une martingale conforme, X 6quivalente sur A a une martingale conforme. ticulier est rele- si martingale X est con- forme. D6monstration Reprenons les que chaque d a n s Wn . Z (V~)nE ~ La p a r t i e s e m i - m a r t i n g a l e e s t le thboreme I ( 2 . 7 ) - conditions est n hlors ~quivalente r6union : sur que lemme ( 2 . 5)-Thboreme mats Alors, VI m o n t r e f soit une pour en supposant A ~ une martingale 1), conforme, on p r e n d diff6omorphisme en outre conforme que X =~n ~ Zn,si X-I(v ') n A ~ une martingale n d6nombrable.

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