Formal Power Series and Stochastic Processes

Describes an algebraic aspect of stochastic processes. This volume provides the description of the algebra of the space on one-dimensional Ito processes. It also considers an extension to the multi-dimensional case.

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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.