Probability Measures on Groups VII: Proceedings of a - download pdf or read online

Read Online or Download Probability Measures on Groups VII: Proceedings of a Conference held in Oberwolfach, 24–30 April 1983 PDF

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Additional resources for Probability Measures on Groups VII: Proceedings of a Conference held in Oberwolfach, 24–30 April 1983

Example text

Ceci 54 ach@ve la d~onstration de la proposition et donc du th6or~/ne. LE RF~ULTAT SUR En suivant exactement la m~ne m@thode on peut d6aaontrer un r6sultat analogue sur l'ens6~ble des entiers, dont l'@nonc@ pr6cis est le suivant. e. e. = i, la chine de ~4~kov de t r a n s i t i o n P ~t r~currente sur ~. P/94ARQUES SUPPI/94ENTAIRES D'apr~s Skorokhod toute probabilit~ centr~e sur IR est la loi du mouv~ment brownien arr~t~ ~ un instant (al~atoire) convenable. Ce r@sultat classique permet d' interpreter le th@or~ne d~nontr~ ci-dessus cosine une condition sur une suite croissante de t6~ps d'arr~t Tn suffisante pour que la chaine Xn = W T obtenue n en arr~tant le mouvement brownien aux instants rence Tn, conserve la propri@t~ de r6~mtr- que le mouvement brownien lui-mg~ne poss~de en dimension 1.

2 n°5 (1959), 29-43. [14] F. Schweiger. S. 19 (1969), 89-91. [15] M. Shrader-Frechette. 54, n°2 (1981), 60-63. S. 591 Universit~ Paul Sabatier 118, route de Narbonne 31062 Toulouse Cedex, France. DROITE Y. DERRIENNIC Universit6 de Bretagne Occidentale D@partement de Math~matiques et Informatique BREST Abstract : A direct, elementary, proof is given to the following result : "Let P(x,dy) a transition probability on the real line. Assume that : i) for ii) P and f continuous and baunded, Pf is continuous.

Exp Cs (~t1~O) : e~p(s (@~tlv)) ~e~p (s (~tlvC~ ~)) If there exist the measures ~Is and exp(~) such that 34 lim n exp(s n /~t I = f s n = f s *exp(OIv * then (6) and Lelmmas 2 and 3 imply t h a t supp(e)~v c ~ F ~ . Now, let ~at) t) 0 be a semigroup of symmetric measures. Let us choose and fix a sequence of symmetric neighbourhoods of the identity Uk~{e ~Repeating the above arguments for the sets UI, U ~ U 2 , U2\U3,... we obtain: [a} a sequence of finite measures {h/k)k such that supp(~1)~U I and supp(~ G Uk_1 \ Uk ' k=2,3 .....

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