A note on asymptotic behavior of critical Galton–Watson processes with immigration

Asymptotic Behavior of Multi-type Nearly Critical Galton–watson Processes with Immigration

where {ξn,j , εn: n, j ∈ N} are independent random variables with nonnegative integer values such that for each n ∈ N, {ξn,j : j ∈ N} are identically distributed. We can interpret Xn as the number of individuals in the n-th generation of a population, ξn,j is the number of offsprings produced by the j-th individual belonging to the (n− 1)-th generation, and εn is the number of immigrants in the...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

asymptotic behavior of multivariate reward processes with nonlinear reward functions

A Note on the Asymptotic Behavior of Conditional Extremes

Suppose (X1,Zl)"'" (Xn,Zn) are LLd. as (X,Z). Let Mn,k be the maximum of all Z. 's for which X. is among the k-nearest neighbors of X=xO' It is shown that M k has the lI , same asymptotic distribution as the maximum of k LLd. copies of the random variable Z given X=xO' Hence, the asymptotic results for Li.d. observations are applicable to this· situation as well. Key' words: nearest neighbor, c...

A note on multitype branching processes with immigration in a random environment

We consider a multitype branching process with immigration in a random environment introduced by Key in [12]. It was shown by Key that the branching process is subcritical in the sense that it converges to a proper limit law. We complement this result by a strong law of large numbers and a central limit theorem for the partial sums of the process. In addition, we study the asymptotic behavior o...