Summary: Generalized chaos decomposition for
L´evy processes
Michael Anshelevich
February 20, 2004
{B(t) : t [0, )} = Brownian motion, gaussian pro-
cess with independent stationary increments.
On a probability space (, , P) with generated by
{B(t)}.
"Functionals" of {B(t)}: B(1)2+B(2), max1t2 B(t),
etc.
Square-integrable functionals: elements
F L2(, , P).
1
Theorem. (Wiener?) Any such F can be written as a
multiple stochastic integral
F =

n=0

0

Source: Anshelevich, Michael - Department of Mathematics, Texas A&M University

Collections: Mathematics