Memoryless representation of Markov processes

Memoryless processes hold many theoretical and practical advantages. They are easy to describe, analyze, store and encrypt. They can also be seen as the essence of a family of regression processes, or as an innovation process triggering a dynamic system. The Gram-Schmidt procedure suggests a linear sequential method of whitening (decorrelating) any stochastic process. Applied on a Gaussian process, memorylessness (that is, statistical independence) is guaranteed. It is not clear however, how to sequentially construct a memoryless process from a non-Gaussian process. In this paper we present a non-linear sequential method to generate a memoryless process from any given Markov process under varying objectives and constraints. We differentiate between lossless and lossy methods, closed form and algorithmic solutions and discuss the properties and uniqueness of our suggested methods.