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Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 2, Pages 247–274 (Mi tvp3917)  

This article is cited in 16 scientific papers (total in 16 papers)

Skew Convolution Semigroups and Related Immigration Processes

Zeng-Hu Li

Beijing Normal University

Abstract: A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give a 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 insight into trajectory structures of the immigration process. Some well-known results on excessive measures are formulated in terms of stationary immigration processes.

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

DOI: https://doi.org/10.4213/tvp3917

Full text: PDF file (3142 kB)

English version:
Theory of Probability and its Applications, 2002, 46:2, 274–297

Bibliographic databases:

Received: 24.03.1999

Citation: Zeng-Hu Li, “Skew Convolution Semigroups and Related Immigration Processes”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 247–274; Theory Probab. Appl., 46:2 (2002), 274–297

Citation in format AMSBIB
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\paper Skew Convolution Semigroups and Related Immigration Processes
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\pages 247--274
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\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 2
\pages 274--297
\crossref{https://doi.org/10.1137/S0040585X97978890}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dawson D.A., Gorostiza L.G., Li Zenghu, “Nonlocal branching superprocesses and some related models”, Acta Appl. Math., 74:1 (2002), 93–112  crossref  mathscinet  zmath  isi  scopus
    2. Dawson D.A., Li Zenghu, “Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions”, Probab. Theory Related Fields, 127:1 (2003), 37–61  crossref  mathscinet  zmath  isi  scopus
    3. Li Zenghu, Wang Zikun, “Generalized Mehler semigroups and Ornstein–Uhlenbeck processes arising from superprocesses over the real line”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 7:4 (2004), 591–605  crossref  mathscinet  zmath  isi  scopus
    4. Fu Zongfei, Li Zenghu, “Measure-valued diffusions and stochastic equations with Poisson process”, Osaka J. Math., 41:3 (2004), 727–744  mathscinet  zmath  isi
    5. Dawson D.A., Li Zenghu, Schmuland B., Sun Wei, “Generalized Mehler semigroups and catalytic branching processes with immigration”, Potential Anal., 21:1 (2004), 75–97  crossref  mathscinet  zmath  isi  scopus
    6. Dawson D.A., Li Zenghu, “Non-differentiable skew convolution semigroups and related Ornstein–Uhlenbeck processes”, Potential Anal., 20:3 (2004), 285–302  crossref  mathscinet  zmath  isi  scopus
    7. Li Zenghu, Wang Hao, Xiong Jie, “Conditional log-Laplace functionals of immigration superprocesses with dependent spatial motion”, Acta Appl. Math., 88:2 (2005), 143–175  crossref  mathscinet  zmath  isi  scopus
    8. Dawson D.A., Li Zenghu, “Skew convolution semigroups and affine Markov processes”, Ann. Probab., 34:3 (2006), 1103–1142  crossref  mathscinet  zmath  isi  elib  scopus
    9. Li Zenghu, Wang Hao, Xiong Jie, “Conditional entrance laws for superprocesses with dependent spatial model”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 11:2 (2008), 259–278  crossref  mathscinet  zmath  isi  scopus
    10. Hazod W., “Mehler semigroups, Ornstein–Uhlenbeck processes and background driving Lévy processes on locally compact groups and on hypergroups”, Semigroup Forum, 83:2 (2011), 214–240  crossref  mathscinet  zmath  isi  elib  scopus
    11. Li Z., “Path-Valued Branching Processes and Nonlocal Branching Superprocesses”, Ann. Probab., 42:1 (2014), 41–79  crossref  mathscinet  zmath  isi  scopus
    12. Ren Ya.-X., Song R., Zhang R., “Central Limit Theorems For Super Ornstein–Uhlenbeck Processes”, Acta Appl. Math., 130:1 (2014), 9–49  crossref  mathscinet  zmath  isi  scopus
    13. Duquesne T. Labbe C., “On the Eve Property For Csbp”, Electron. J. Probab., 19 (2014), 6, 1–31  crossref  mathscinet  isi  scopus
    14. Ren Ya.-X., Song R., Zhang R., “Central Limit Theorems For Supercritical Superprocesses”, Stoch. Process. Their Appl., 125:2 (2015), 428–457  crossref  mathscinet  zmath  isi  scopus
    15. Ren Ya.-X., Song R., Zhang R., “Functional Central Limit Theorems for Supercritical Superprocesses”, Acta Appl. Math., 147:1 (2017), 137–175  crossref  mathscinet  zmath  isi  scopus
    16. Wang L., “Central Limit Theorems For Supercritical Superprocesses With Immigration”, J. Theor. Probab., 31:2 (2018), 984–1012  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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