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Parameter estimation in two-type continuous-state branching processes with immigration
Institution:1. School of Mathematics and Statistics, Guangdong University of Finance & Economics, Guangzhou 510320, PR China;2. Department of Mathematics, Jinan University, Guangzhou 510630, PR China;1. Department of Mathematics, Vanderbilt University, United States;2. Department of Statistics, University of Florida, United States;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
Abstract:We study the parameter estimation of two-type continuous-state branching processes with immigration based on low frequency observations at equidistant time points. The ergodicity of the processes is proved. The estimators are based on the minimization of a sum of squared deviation about conditional expectations. We also establish the strong consistency and central limit theorems of the conditional least squares estimators and the weighted conditional least squares estimators of the drift and diffusion coefficients based on low frequency observations.
Keywords:Two-type continuous-state branching process with immigration  Stochastic differential equation  Conditional least squares estimator  Weighted conditional least squares estimator  Consistency  Central limit theorem
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