Generalized holomorphic processes and differentiability

Ely Merzbach; David Nualart

doi:10.1007/bf01051875

Generalized holomorphic processes and differentiability

Ely Merzbach, David Nualart

Department of Mathematics

University of Barcelona

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Holomorphic processes are studied when the parameter set is a general finite atomless separable measure space, using the differentiation operator and Malliavin calculus. Generalized martingales are connected with differentiable processes. In the two-parameter case, these methods give a new simpler proof of the characterization of holomorphic processes by power series expansion.

Original language	English
Pages (from-to)	419-432
Number of pages	14
Journal	Journal of Theoretical Probability
Volume	2
Issue number	4
DOIs	https://doi.org/10.1007/bf01051875
State	Published - Oct 1989

Keywords

Clark's formula
Holomorphic process
Malliavin calculus
differentiation operator
generalized martingale

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10.1007/bf01051875

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abstract = "Holomorphic processes are studied when the parameter set is a general finite atomless separable measure space, using the differentiation operator and Malliavin calculus. Generalized martingales are connected with differentiable processes. In the two-parameter case, these methods give a new simpler proof of the characterization of holomorphic processes by power series expansion.",

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AU - Nualart, David

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AB - Holomorphic processes are studied when the parameter set is a general finite atomless separable measure space, using the differentiation operator and Malliavin calculus. Generalized martingales are connected with differentiable processes. In the two-parameter case, these methods give a new simpler proof of the characterization of holomorphic processes by power series expansion.

KW - Clark's formula

KW - Holomorphic process

KW - Malliavin calculus

KW - differentiation operator

KW - generalized martingale

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JO - Journal of Theoretical Probability

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Generalized holomorphic processes and differentiability

Abstract

Keywords

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