Abstract A properly scaled critical Galton–Watson process converges to a continuous state critical branching process <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>ξ</mi> <mo>⁢</mo> <mrow> <mo stretchy="false">(</mo> <mo lspace="4.2pt" rspace="4.2pt">⋅</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>ξ</mi> <mo>⁢</mo> <mrow> <mo stretchy="false">(</mo> <mo lspace="4.2pt" rspace="4.2pt">⋅</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </math> as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping generations and...

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...

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...