Jan 6, 2003 · The functionals are iterated integrals of the basic martingales, similar to the multiple iterated integrals of Itô and can be also thought of as ...

The purpose of the present paper is to continue Ito's work in this direction by introducing and analyzing the basic functionals in terms of which the multiple ...

A set of functionals of general square-integrable martingales is presented which, in the case of independent-increments processes, is orthogonal and ...

A recursive formula for these functionals in terms of the basic martingale and of lower order functionals is given, and several connections with the theory of ...

The functionals are iterated integrals of the basic martingales, similar to the multiple iterated integrals of Itô and can be also thought of as being the ...

TL;DR: In this article, a functional Fourier series is developed with emphasis on applications to the nonlinear systems analysis, and Fourier kernels are ...

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Mar 13, 2023 · Then X=(Xt)t≥0 is said to have orthogonal increments if Xt∈L2(Ω,A,P) and if E(Xt−Xs)(Xt′−Xs′)=0 for all [s,t],[s′,t′]⊆[0,∞) such that [s,t]∩[s′, ...

A Stochastic process has independent increments if for all s, t ∈ R+ with s<t, the random variable Xt − Xs is independent of Fs. In most general form we define ...

A stochastic process can be represented as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function ...