2011/08/05 by Kenji Handa, Handa, Kenji
Economics, Econometrics and Finance · Mathematics · #60J75 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1108.1289
openalex publication_date 2011/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class of models, we prove that every generalized gamma convolution is a stationary distribution of the process with suitably chosen branching mechanism and with continuous immigration. For such non-reversible processes, the strong sector condition is discussed in terms of a characteristic called the Thorin measure. In addition, some connections with notion from noncommutative probability theory will be pointed out through calculations involving the Stieltjes transform.