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Stochastic equations for two-type continuous-state branching processes with immigration and competition
Institution:1. Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th street, PH C104, Bloomington, IN, 47405, USA;2. Department of Epidemiology and Biostatistics, University of Georgia, Athens, GA 30602, USA;3. Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, PO Box 750332, Dallas, TX 75275-0332, USA;1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, China;2. School of Economics and Management, Southeast University, Nanjing, 210096, China;3. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania;4. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius LT-08663, Lithuania;1. Department of Mathematics, Vanderbilt University, United States;2. Department of Statistics, University of Florida, United States;1. Université de Rouen, LITIS EA 4108, Avenue de l’Université, BP 12, 76801 Saint-Étienne-du-Rouvray, France;2. Rutgers University, Department of Statistics, 561 Hill Center, Busch Campus, Piscataway, NJ 08854-8019, USA
Abstract:A class of two-type continuous-state branching processes with immigration and competition is constructed as the solution of a jump-type stochastic integral equation system. We first show that the stochastic equation system has a pathwise unique non-negative strong solution and then prove the comparison property of the solution.
Keywords:Continuous-state branching process  Immigration  Competition  Stochastic integral equation  Strong solution  Comparison property
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