Asymptotic properties of singularly perturbed Markov chains having measurable and/or continuous generators are developed in this work. The Markov chain under consideration has a finite-state space and is allowed to be nonstationary. Its generator consists of a rapidly varying part and a slowly...

In this paper, we consider a class of nonlinear autoregressive (AR) processes with state-dependent switching, which are two-component Markov processes. The state-dependent switching model is a nontrivial generalization of Markovian switching formulation and it includes the Markovian switching as...

The Robbins-Monto processes in a Hilbert space are considered in this work. A nonlinear mapping f is treated instead of the usual linearity assumption. A modified process with varying truncations is analyzed, and asymptotic properties are investigated. Convergence as well as necessary and...