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Formal Power Series and Stochastic Processes: Noncommutative Formal Power Series and Chaotic Representation of Stochastic Processes
Eva Riccomagno 
Publisher: Imperial College Press
ISBN10: 1860947700 ISBN13: 9781860947704 DDC: 500 Edition: Hardcover; 2010-03-31

Summary

This volume describes an algebraic aspect of stochastic processes. It is based on the link between noncommutative formal power series and the chaotic representation of stochastic processes. Volterra series expansion and formal power series are connected in the notion of causal functional for deterministic inputs. Here, the description of the algebra of the space on one-dimensional Ito processes is at the core of the monograph. Ito processes are characterised as classical iterated integral series. An extension to the multi-dimensional case is considered. The investigation of similar algebraic aspects of Levy processes is based on their chaotic representation. Classical arguments are employed throughout. A major application of the theory is the solution by series of differential equations.

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