Continuous-Time Higher Order Markov Chains: Formulation and Parameter Estimation

TL;DR

This paper introduces a novel continuous-time formulation of higher order Markov processes using stochastic differential equations, along with a maximum likelihood parameter estimation method, enhancing modeling flexibility.

Contribution

It presents the first continuous-time higher order Markov process model and a corresponding parameter estimation technique, bridging a gap in stochastic process modeling.

Findings

New continuous-time higher order Markov model formulated

Maximum likelihood estimation method developed for parameters

Potential for improved data modeling in various disciplines

Abstract

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data better. However most higher order Markov models are discrete. Here, we propose a novel continuous-time formulation of higher order Markov processes, as stochastic differential equations, and propose a method of parameter estimation by maximum likelihood methods.