The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the ...The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).展开更多
Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-vained immigration diffusion process are studied,which lead to the general...Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-vained immigration diffusion process are studied,which lead to the generalized Ornstein-Uhlenbeck diffusion defined by a Langevin equation ofthe type of [1]. The fluctuation limit theorems cover all dimension numbers and give physicalinterpretations to the parameters appearing in the equation.展开更多
A superprocess is a continuous analogue of an infinite particle branching pro-cess.The branching mechanism of a superprocess is a function ψ(λ)of the form(cf.[3])
This paper proves a 1-1 correspondence between minimal probability entrance laws for the superprocess and entrance laws for its underlying process. From this the author deduces that an infinitely divisible probability...This paper proves a 1-1 correspondence between minimal probability entrance laws for the superprocess and entrance laws for its underlying process. From this the author deduces that an infinitely divisible probability entrance law for the superprocess is uniquely determined by an infinitely divisible probability measure on the space of the underlying entrance laws. Under an additional condition, a characterization is given for all entrance laws for the superprocess, generalizing the results of Dynkin (1989). An application to immigration processes is also discussed.展开更多
Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurabl...Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurable functions on E and B(E)^+ denotes the subspace of B(E) comprising non-negative elements. Let M(E) be the totality of finite measures on (E, (?)(E)). Topologize M(E) by the weak convergence topology, so it also becomes a展开更多
A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equati...A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.展开更多
基金the National Natural Science Foundation of China!(No.19361060)and the Mathematical Center of the State Education Commission of
文摘The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).
文摘Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-vained immigration diffusion process are studied,which lead to the generalized Ornstein-Uhlenbeck diffusion defined by a Langevin equation ofthe type of [1]. The fluctuation limit theorems cover all dimension numbers and give physicalinterpretations to the parameters appearing in the equation.
文摘A superprocess is a continuous analogue of an infinite particle branching pro-cess.The branching mechanism of a superprocess is a function ψ(λ)of the form(cf.[3])
文摘This paper proves a 1-1 correspondence between minimal probability entrance laws for the superprocess and entrance laws for its underlying process. From this the author deduces that an infinitely divisible probability entrance law for the superprocess is uniquely determined by an infinitely divisible probability measure on the space of the underlying entrance laws. Under an additional condition, a characterization is given for all entrance laws for the superprocess, generalizing the results of Dynkin (1989). An application to immigration processes is also discussed.
文摘Suppose that E is a Lusin topological space. We let (?)(E) denote the σ-algebra on E generated by all open sets, which is referred to as the Borel σ-algebra on E. B(E) denotes the set of all bounded (?)(E)-measurable functions on E and B(E)^+ denotes the subspace of B(E) comprising non-negative elements. Let M(E) be the totality of finite measures on (E, (?)(E)). Topologize M(E) by the weak convergence topology, so it also becomes a
基金supported by the National Key R&D Program of China(2020YFA0712900)the National Natural Science Foundation of China(11531001).
文摘A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.
