Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional ap...Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensionl stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.展开更多
Recently, the theory of valuations on function spaces has been rapidly growing. It is more general than the classical theory of valuations on convex bodies. In this paper, all continuous, SL(n) and translation invaria...Recently, the theory of valuations on function spaces has been rapidly growing. It is more general than the classical theory of valuations on convex bodies. In this paper, all continuous, SL(n) and translation invariant valuations on concave functions and log-concave functions are completely classified, respectively.展开更多
In this paper, by using the W-transform of an operator on white noise functionals, we establish a general characterization theorem for operators on white noise functionals in term of growth condition. We also discuss ...In this paper, by using the W-transform of an operator on white noise functionals, we establish a general characterization theorem for operators on white noise functionals in term of growth condition. We also discuss convergence of operator sequences.展开更多
文摘Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensionl stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.
基金Supported by Foundation of China Scholarship Council(201808430267)the Education Department of Hunan Province(16C0635)the Natural Science Foundation of Hunan Province(2017JJ3085)
文摘Recently, the theory of valuations on function spaces has been rapidly growing. It is more general than the classical theory of valuations on convex bodies. In this paper, all continuous, SL(n) and translation invariant valuations on concave functions and log-concave functions are completely classified, respectively.
文摘In this paper, by using the W-transform of an operator on white noise functionals, we establish a general characterization theorem for operators on white noise functionals in term of growth condition. We also discuss convergence of operator sequences.
