We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting ...We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.展开更多
It is proved by the theory of semigroup that the Ornstein-Uhlenbeck type process with jumps can arise from the fluctuation limit of a sequence of Jirina processes with immigration under suitable moments conditions.
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
基金Supported by National Natural Science Foundation of China(Grant No.11126052)
文摘We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.
基金Supported in part by National Natural Science Foundation of China (Grant No. 10771070)
文摘It is proved by the theory of semigroup that the Ornstein-Uhlenbeck type process with jumps can arise from the fluctuation limit of a sequence of Jirina processes with immigration under suitable moments conditions.
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.
