Properties Of M-Term Algebraic Sum Of Image Set Of N-Parameter D-Dimension Generalized Wiener Process

As we know ,the word " Fractal " was initiated by Mandelbrot.B.B in the " Fractals :Forms,Chance and Dimension,Freeman " in 1977.Since then ,Fractals has been quickly developed on account of the development of theory and the need of application ,among which the fracltal theory of Sctochastic Field is one of its important branches .There are some conclusions with respect to algebraic sum of Stochastic Field .N-parameter d-dimension generalized Wiener process is the extension of Brown Motion in the sense of multiparameter ,and plays an indispensable role in Stochastic Field . Let be a N-parameter d-dimension generalized Winner process , is called m-term algebraic sum of image set of W.Chen Zhenlong and Liu Sanyang studied Hausdorff dimension and Packing dimension and the existence of interior points of under the condition of i ≤ m) being compact set and others . Considering σ-stability of Hausdorff dimension and Packing dimension and numerable covering of Borel sets ,we draw the more general conclusions on Hausdorff dimension and Packing dimension and the existence of interior points of W{E₁) W(E₂) W(E_m) under the condition of E_i R₊^N (1 ≤ i ≤ m) being Borel sets and others .This paper concludes such contents:As the introduction in Chapter 1,preliminary knowledge is interpreted;the present studying backgrounds of N-parameter d- dimension gengeralized Wiener process is reviewed briefly;conditions of major theories and theories of this paper are proposed .In Chapte 2, we discuss the studying background of Hausdorff dimension and Packing dimension of m-term algebraic sum of image sets of N-parameter d-dimension generalized Wiener process ,and the major theories have been strictly-proved .In Chapter 3,some people's theorems about the existence of interior points of image sets of (iV, d) Stochastic Fields and the author's main theorem and its proof on the existence of interior points of m-terrn algebraic sum of image sets of N-parameter d-dimension generalized Wiener process construct this chapter.Chapter 4 begins a summation of methods used above ,and points the way to solve more general problems with these methods .