In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stocha...In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.展开更多
In this article the notion of quasi symmetry is introduced.It is proved that the quasi symmetry is equivalent to the uniqueness of invariant measure of Lévy processes in some sense.Moreover,the relationship bet...In this article the notion of quasi symmetry is introduced.It is proved that the quasi symmetry is equivalent to the uniqueness of invariant measure of Lévy processes in some sense.Moreover,the relationship between ratio limits and invariant measures is studied.展开更多
In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at ...In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.展开更多
In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potent...In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.展开更多
基金Supported by the Natural Science Foundation of Henan Province(2004601018).
文摘In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
文摘In this article the notion of quasi symmetry is introduced.It is proved that the quasi symmetry is equivalent to the uniqueness of invariant measure of Lévy processes in some sense.Moreover,the relationship between ratio limits and invariant measures is studied.
文摘In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.
文摘In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.
