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2005年07月12日

【期刊论文】MEASURE-VALUED BRANCHING PROCESSES WITH IMMIGRATION

李增沪， Zeng-Hu LI

Stochastic Processes and their Applications 43 (1992), 249-264.，-0001，（）：

-1年11月30日

Starting from the cumulant semigroup of a measure-valued branching process, we construct the transition probabilities of some Markov process Y (β) = (Yt (β), t ∈ R), which we call a measure-valued branching process with discrete immigration of unitβ. The immigration of Y (β) is governed by a Poisson random measure р on the time-distribution space and a probability generating function h; both depending on β. It is shown that, under suitable hypotheses, Y (β) approximates to a Markov process Y = (Yt, t ∈ R) as β→ 0+. The latter is the one we call a measure-valued branching process with immigration. The convergence of branching particle systems with immigration is also studied.

measure-valued branching process， immigration， particle system， superprocess， weak convergence

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2005年07月12日

【期刊论文】Generalized Mehler Semigroups and Catalytic Branching Processes with Immigration1

李增沪， DONALD A. DAWSON， ZENGHU LI， BYRON SCHMULAND and WEI SUN

Potential Analysis 21 (2004), 1: 75-97，-0001，（）：

-1年11月30日

摘要

Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose characteristic functional is not necessarily di

generalized Mehler semigroup， skew convolution semigroup， Ornstein-Uhlenbeck process， catalytic branching superprocess， immigration， fluctuation limit.，

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2005年07月12日

【期刊论文】Construction of Immigration Superprocesses with Dependent Spatial Motion from One-Dimensional Excursions

李增沪， DONALD A. DAWSON， ZENGHU LI

Probability Theory and Related Fields 127 (2003), 37-61.，-0001，（）：

-1年11月30日

摘要

A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions.

superprocess， dependent spatial motion， immigration， excursion， stochastic equation， Poisson random measure.，

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2005年07月12日

【期刊论文】ORNSTEIN-UHLENBECK TYPE PROCESSES AND BRANCHING PROCESSES WITH IMMIGRATION

李增沪， Zeng-Hu LI

Journal of Applied Probability 37 (2000), 627-634.，-0001，（）：

-1年11月30日

摘要

It is shown that an Ornstein-Uhlenbeck type process associated with a spectrally positive L'evy process can be obtained as the fluctuation limits of both discrete state and continuous state branching processes with immigration.

branching process， immigration， Levy process， Ornstein-Uhlenbeck type process， fluctuation limit

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2005年07月12日

【期刊论文】ASYMPTOTIC BEHAVIOR OF CONTINUOUS TIME AND STATE BRANCHING PROCESSES

李增沪， Zeng-Hu LI*

Journal of the Australian Mathematical Society Series A 68 (2000), 68-84.，-0001，（）：

-1年11月30日

摘要

We prove some limit theorems for continuous time and state branching processes. The non-degenerate limit laws are obtained in critical and non-critical cases by conditioning or introducing immigration processes. The limit laws in non-critical cases are characterized in terms of the canonical measure of the cumulant semigroup. The proofs are based on estimates of the cumulant semigroup derived from the forward and backward equations, which are easier than the proofs in the classical setting.

branching processes， continuous time， continuous sate， conditioning， immigration， limit theorem

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