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2005年07月12日

【期刊论文】Generalized Mehler Semigroups and Ornstein-Uhlenbeck Processes Arising from Superprocesses over the Real Line 1

李增沪， Zenghu Li and Zikun Wang

Infinite Dimensional Analysis, Quantum Probability and Related Topics 7 (2004), 4: 591-605.，-0001，（）：

-1年11月30日

We study the fluctuation limits of a class of superprocesses with dependent spatial motion on the real line, which give rise to some new Ornstein-Uhlenbeck processes with values of Schwartz distributions.

superprocess with dependent spatial motion， fluctuation limit， Ornstein-Uhlenbeck process， generalized Mehler semigroup

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2005年07月12日

【期刊论文】A Degenerate Stochastic Partial Di erential Equation for Superprocesses with Singular Interaction

李增沪， Zenghu Li， Hao Wang， Jie Xiong

Probability Theory and Related Fields 130 (2004), 1: 1-17.，-0001，（）：

-1年11月30日

摘要

The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial di erential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measurevalued process which is the unique strong solution of a reconstructed, associated SDSPDE.

coalescing Brownian motion， scaling limit， purely atomic superprocess， interaction， stochastic partial dierential equation， strong solution， pathwise uniqueness.，

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2005年07月12日

【期刊论文】SKEW CONVOLUTION SEMIGROUPS AND RELATED IMMIGRATION PROCESSES 1

李增沪， Zeng-Hu LI

Theory of Probability and its Applications 46 (2002), 274-296.，-0001，（）：

-1年11月30日

摘要

A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give characterization for a general inhomogeneous skew convolution semigroup in terms of probability entrance laws. The related immigration process is constructed by summing up measure-valued paths in the Kuznetsov process determined by an entrance rule. The behavior of the Kuznetsov process is then studied, which provides insights into trajectory structures of the immigration process. Some well-known results on excessive measures are formulated in terms of stationary immigration processes.

measure-valued branching process， superprocess， immigration process， skew convolution semigroup， entrance law， entrance rule， excessive measure， Kuznetsov measure

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2005年07月12日

【期刊论文】Non-di erentiable Skew Convolution Semigroups and Related Ornstein-Uhlenbeck Processes

李增沪， DONALD A. DAWSON， ZENGHU LI

Potential Analysis 20 (2004), 285-302.，-0001，（）：

-1年11月30日

摘要

It is proved that a general non-di erentiable skew convolution semigroup associated with a strongly continuous semigroup of linear operators on a real separable Hilbert space can be extended to a di erentiable one on the entrance space of the linear semigroup. A cadl ag strong Markov process on an enlargement of the entrance space is constructed from which we obtain a realization of the corresponding Ornstein-Uhlenbeck process. Some explicit characterizations of the entrance spaces for special linear semigroups are given.

skew convolution semigroup， dierentiable extension， generalized Ornstein-Uhlenbeck process， right continuous realization.，

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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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