Generalization Of Local Times For Gaussian Integators

Gaussian integrators were first introduced by Dorogovtsev[1]as a generalization of Wiener process.In particular,he proved that a centered Gaussian process{Y（t）,t∈[0,1]}is a Gaussian integrator if and only if there exist a continuous linear operator A on L²（[0,1]）and a Gaussian white noiseξdefined on the same space such that Y（t）=(AI_[0,1],ξ),t∈[0,1],and that fractional Brownian motion with Hurst index H>1/2is a Gaussian integrator.Furthermore,Izyumtseva[9]studied some of the local time properties for a class of Gaussian integrators.However,she needs the associated operator A to be invertible,which excludes fractional Brownian motion with Hurst index H>1/2 from the class.In this thesis,we study local time properties for a class of Gaussian integrators,including fractional Brownian motion with Hurst index H>1/2,by relaxing the restric-tion on operator A from continuously invertible to quasi-coercive.One of our main tools in our derivation is the notion of strong local nondeterminism of the Gaussian integrators.We also study the extension of local nondeterminism to r distinct points for a class of Gaussian integrators,such as fractional Brownian motion with Hurst index H>1/2.