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

Music City Center 

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. A random process with stationary increments is a stochastic process where its distribution of the increments only depends on its temporal or spatial intervals. On the other hand, an intrinsic random function is a flexible family of non-stationary processes where the process is assumed to have lower monomials as its mean and the transformed process becomes stationary. This research illustrates the relationship between these two concepts of stochastic processes and shows that, under certain conditions, they are equivalent on the real line.

intrinsic random function

random process with stationary increment

non-stationary random process

spatial statistics

time series 

Section on Statistics and the Environment