Random Processes with Stationary Increments and Intrinsic Random Functions on the Real Line

TL;DR

This paper explores the relationship between random processes with stationary increments and intrinsic random processes, demonstrating their equivalence under certain conditions on the real line, thus broadening understanding of non-stationary processes.

Contribution

It clarifies the connection between two important classes of non-stationary processes and establishes conditions under which they are equivalent.

Findings

Shows equivalence of the two process classes under specific conditions

Provides theoretical insights into non-stationary process modeling

Enhances understanding of stochastic process relationships

Abstract

Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely related to each other. This paper illustrates the relationship between these two concepts of stochastic processes and shows that, under certain conditions, they are equivalent on the real line.