Natural decomposition of processes and weak Dirichlet processes

Details Natural decomposition of processes and weak Dirichlet processes Natural decomposition of processes and weak Dirichlet processes

2004-03-26

arxiv.org/abs/math/0403461v2

Mathematics

Probability

mars 2004

Scientific paper

A class of stochastic processes, called "weak Dirichlet processes", is introduced and its properties are investigated in detail. This class is much larger than the class of Dirichlet processes. It is closed under C^1$-transformations and under absolutely continuous change of measure. If a weak Dirichlet process has finite energy, as defined by Graversen and Rao, its Doob-Meyer type decomposition is unique. The developed methods have been applied to a study of generalized martingale convolutions.

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