Stochastic Analysis And Paramenter Estimation Of Rosenblatt Process

The article is mainly about studying the stochastic integral and the related least square estimation of the Rosenblatt process.The Rosenblatt process can be written as follows: in which the operator I is defined on set of functions f:f:[0, T]→R,and takes values in the set of functions:g:[0,T]2→R2and it is given by: The constants are: First of all,we define the wick integral of the Rosenblatt process and then study the Ito formula in the form of skorohod integral: in which,Nt=ucp-limε→0(2Bε1-Cε2),Bε1andCε2are as follows: We mainly study the Ito formula and its expanded form when f(x)=x4...and until f(x)=x(n).Fianlly,we study the O-U process which is driven by the Rosenblatt process: dXt=-θXtdt+εdZt, t≥0 andθis the unknown parameter.We establish the following least square estimator. our goal is to prove thatθn,ε→θin probability.