Asymptotic behavior of unstable INAR(p) processes

Asymptotic behavior of unstable INAR(p) processes

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unst...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

asymptotic behavior of multivariate reward processes with nonlinear reward functions

The asymptotic behavior of fragmentation processes

The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the ranked sequence of the masses of the pieces of an object that falls apart randomly as time passes. We investigate their behavior as t → ∞. Roughly, we show that the rate of decay of the ℓ p-norm (where p > 1) is exponential when the index of self-similarity α is 0, polynomial wh...

The Asymptotic Behavior of Certain Birth Processes∗

We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and variance.