Hilbert Space Valued Generalized Random Processes – Part I
نویسنده
چکیده
Generalized random processes by various types of continuity are considered and classified as generalized random processes (GRPs) of type (I) and (II). Structure theorems for Hilbert space valued generalized random processes are obtained: Series expansion theorems for GRPs (I) considered as elements of the spaces L(A, S(H)−1) are derived, and structure representation theorems for GRPs (II) on K{Mp}(H) on a set with arbitrary large probability are given. AMS Mathematics Subject Classification (2000): 60G20, 60H40, 46N30, 46F25
منابع مشابه
Hilbert Space Valued Generalized Random Processes – Part Ii
Generalized random processes (GRPs) were classified as GRPs (I) and (II) in Part I of this paper. Now we focus our attention om GRPs (I), i.e. linear continuous mappings from a certain space of test functions to some space of classical or generalized random variables. The paper is organized in the following manner: In the introductory section (Section 1) we provide some basic terminology and no...
متن کاملSome Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. ...
متن کاملStochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کاملA System of Random Nonlinear Variational Inclusions Involving Random Fuzzy Mappings and H(,)-Monotone Set-Valued Mappings
We introduce and study a new system of random nonlinear generalized variational inclusions involving random fuzzy mappings and set-valued mappings with H ·, · -monotonicity in two Hilbert spaces and develop a new algorithm which produces four random iterative sequences. We also discuss the existence of the random solutions to this new kind of system of variational inclusions and the convergence...
متن کاملCommon Fixed Point Results on Complex-Valued $S$-Metric Spaces
Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...
متن کامل