HOLOMORPHIC PROCESSES IN BANACH-SPACES AND BANACH-ALGEBRAS

JOURNAL OF MULTIVARIATE ANALYSIS

卷:48

Article

RANSFORD, TJ

关键词: ANALYTIC MULTIFUNCTION;    BROWNIAN MOTION;    HOLOMORPHIC PROCESS;    CONFORMAL MARTINGALE;    SUBMARTINGALE;   

DOI  :  10.1006/jmva.1994.1008

来源: Elsevier

【 摘 要 】

The main result is that if F is an analytic multifunction and B(t) is a complex Brownian motion, then F(B(t)) is a subholomorphic process. It has previously been shown that such processes enjoy many interesting sample-path properties. As special cases of the theorem above, we recover f holomorphic double line arrow pointing right f(B(t)) is a local conformal martingale, phi subharmonic double line arrow pointing right phi(B(t)) is a local submartingale. We also prove a stochastic form of Rado's theorem, and a holomorphic selection theorem for convex-valued subholomorphic processes of a nature quite different from the usual type of measurable selection theorem. (C) 1994 Academic Press, Inc.

【 授权许可】

Free