ATTRACTING AND QUASI-INVARIANT SETS OF STOCHASTIC NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this article, we investigate a class of stochastic neutral partial functional differ- ential equations. By establishing new integral inequalities, the attracting and quasi-invariant sets of stochastic neutral partial functional differential equations are obtained. The results in [15, 16] are generalized and improved.

Quasi-invariant transformations on the path space over a manifold

Some interesting quasi-invariant transformations on the path space over a Riemannian manifoldare investigated. The results improve some previous ones.

Structure of Quasi-Invariant Vector Spaces

Let V be a vector space over a field F and G a group of linear transformations in V. It is proved in this note that for any subspace U (V, if dimU/(U∩ g(U))≤ 1, for any g∈G, then there is a g∈ G such that U∩g(U) is a G-invariant subspace, or there is an x∈ V\U such that U + <x> is a G-invariant subspace. So a vector-space analog of Brailovsky's results on quasi-invariant sets is given.

THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a^2 in the case of n > 2.

Zero-based subspaces and quasi-invariant subspaces of the Bargmann-Fock space

We use the Weierstrass a-function associated with a lattice in the complex plane to construct finite dimensional zero-based subspaces and quasi-invariant subspaces of given index in the Bargmann-Fock space.

ON BANACH SUPPORT OF AN ERGODIC AND QUASI-INVARIANT MEASURE

Concerning the study of Banach support for the sample space of a random process, the idea can go back to the penetrating investigation of R. Dudley, V.N. Sudaso and X. Fernique, about Gaussian cylindrical measure. Gross, Ito, Sato and J. Kuelbs have investigated Banach support of a measure which, however, considers essentially Gaussian measure and proves that there exists Banach support for ordinary Gaussian measures. The abstract Wieber space introduced by Gross plays an important role in the study of Gaussian process. The ergodic and quasi-invariant measures investigated in this note are much wider than the abstract Wiener spaces, and the results obtained are stronger than the

Global Attractiveness and Quasi-Invariant Sets of Impulsive Neutral Stochastic Functional Differential Equations Driven by Tempered Fractional Brownian Motion

In this paper,we are concerned with a class of impulsive neutral stochastic functional different equations driven by tempered fractional Brownian motion in the Hilbert space.We obtain the global attracting and quasi-invariant sets of the considered equations driven by tempered fractional Brownian motion B^(α,λ)(t)with 0<α<1/2 andλ>0.In particular,we give some sufficient conditions which ensure the exponential decay in the p-th moment of the mild solution of the considered equations.Finally,an example is given to illustrate the feasibility and effectiveness of the results obtained.

Geodesic flows on path spaces

On the path space over a compact Riemannian manifold, the global existence and the global uniqueness of the quasi-invariant geodesic flows with respect to a negative Markov connection are obtained in this paper. The results answer affirmatively a left problem of Li.

Gamma-Dirichlet algebra and applications

The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. We finish the paper with the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration by exploring the Gamma-Dirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and

Ordered Reproducing Hilbert Spaces over C^2

In this paper, we study the relation between the ordered reproducing Hilbert space and its reproducing kernel. A complete description of a similar and unitary equivalence of two quasi-invariant subspaces generated by polynomials with leading terms is given.