Discrete random processes with memory: Models and applications

Abstract

The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior of proposed random walks, as well as the task of their parameter estimation, are studied both theoretically and with the aid of simulations.

A model and application of binary random sequence with probabilities depending on history

“…An initial analysis of such models performance was provided in Kouřim and Volf [6]. The properties of models were studied, their limit (large sample) properties were derived theoretically, while their behavior in small time horizon was examined graphically and with the aid of simulations.…”