Abstract This is a short survey about asymptotic properties of a supercritical branching process (Z_{n}) with immigration in a stationary and ergodic or independent and identically distributed random environment. We first present basic properties of the fundamental submartingale (W_{n}) , about...

We analyse the mathematical structure of models for large risk portfolios, especially for credit risk models. These risk portfolios are modelled using a multivariate mixture model for the dependence structure between the risks. The dependence structures are characterized by latent variables Θ,...

We consider discrete time Hawkes process which is a class of g-functions. The limit theorems for continuous time Hawkes processes are well known and studied by many authors. In this paper, we study the limit theorems for discrete time Hawkes processes. In particular, we obtain the law of large...

We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals of...

We show that a mixed equilibrium of a semi-anonymous nonatomic game can be used to generate pure-strategy profiles for finite games randomly generated from the type distribution of the nonatomic game. As the numbers of players involved in the finite games increase, the generated profiles will be...

We consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agentsʼ voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting...

Nabil Al-Najjar (2008) showed how games with countably infinite player sets can be used to approximate games with large finite player sets. Unfortunately, we have found an error in the proof of Al-Najjarʼs Theorem 5. In this correction we discuss the error and offer two slightly weaker versions...

The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the...