Quadratic variation of functionals of two-parameter Wiener process

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...

Estimation of quadratic variation for two-parameter diffusions

Abstract In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations [ns] i=1 [nt] j=1 |∆i,jY | of a twoparameter diffusion Y = (Y(s,t))(s,t)∈[0,1]2 observed on a regular grid Gn is an asymptotically normal estimator of the quadratic variation of Y as n goes t...

Time-averaged quadratic functionals of a Gaussian process.

The characterization of a stochastic process from its single random realization is a challenging problem for most single-particle tracking techniques which survey an individual trajectory of a tracer in a complex or viscoelastic medium. We consider two quadratic functionals of the trajectory: the time-averaged mean-square displacement (MSD) and the time-averaged squared root mean-square displac...

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...

Variation of Domain Functionals