Stochastic integral representation of multiplicative operator functionals of a Wiener process
Stochastic integral representation of multiplicative operator functionals of a Wiener process
Let <italic>M</italic> be a multiplicative operator functional of (<italic>X, L</italic>) where <italic>X</italic> is a <italic>d</italic>-dimensional Wiener process and <italic>L</italic> is a separable Hilbert space. Sufficient conditions are given in order that <italic>M</italic> be equivalent to a solution of the linear Itô equation <disp-formula content-type="math/mathml"> \[ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M left-parenthesis …