Quadratic Wiener functionals of square norms on measure spaces

Quadratic Variation of Functionals of Two-Parameter Wiener Process

Let [W(s, t): (s, t) E R+7, R+2 = [0, co) x [0, co), be the standard twoparameter Wiener process defined on a complete probability space (Q, F, P), i.e., a Gaussian stochastic process with EW(s, t) = 0 and EW(s, t) W(s’, t’) = Min(s, s’) Min(t, t’). We shall also assume, as we may do without restricting the generality, that W(s, t; UJ) is sample path continuous, i.e., for each w, W(.; U) is a c...

On the square root of quadratic matrices

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.

Irregular and Simulatable Functionals on Wiener Space

be locally Lipschitz. This occurs in particular when d — 1. In that case it is possible to construct almost sure and L approximations X'(u>) of X(u>) by approximating the Brownian path u> and using the continuity of the Ito mapping (see e.g. [6] [28] [21]). Actually, with or without the Frobenius assumption, direct discretization schemes X' can be constructed which converge in V and for some sc...

Weak Approximations for Wiener Functionals

Abstract. In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions of a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The approximation is given in terms of discrete-jumping filtrations which allow us...

Norms on Quotient Spaces