The Annals of Probability

On transition semigroups of $(A,\Psi )$-superprocesses with immigration

Wilhelm Stannat

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Abstract

We study the global properties of transition semigroups $(p_t^{\nu , \Psi , A})$ of $(A, \Psi )$-superprocesses over compact type spaces with possibly nonzero immigration $\nu$ in various function spaces. In particular, we compare the different rates of convergence of $(p_t^{\nu ,\Psi ,A})$ to equilibrium. Our analysis is based on an explicit formula for the Gateaux derivative of $p_t^{\nu ,\Psi , A} F$.

Article information

Source
Ann. Probab., Volume 31, Number 3 (2003), 1377-1412.

Dates
First available in Project Euclid: 12 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1055425784

Digital Object Identifier
doi:10.1214/aop/1055425784

Mathematical Reviews number (MathSciNet)
MR1989437

Zentralblatt MATH identifier
1043.60076

Subjects
Primary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Secondary: 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx} 60F10: Large deviations 60G57: Random measures 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92D10: Genetics {For genetic algebras, see 17D92}

Keywords
Superprocesses ergodic theorems gradient estimates Gamma processes short-time asymptotics.

Citation

Stannat, Wilhelm. On transition semigroups of $(A,\Psi )$-superprocesses with immigration. Ann. Probab. 31 (2003), no. 3, 1377--1412. doi:10.1214/aop/1055425784. https://projecteuclid.org/euclid.aop/1055425784


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References

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