- #1
copernicus1
- 99
- 0
Can anyone provide references for stochastic processes where future steps do depend on the past state of the system? Most of the material I'm finding deals purely with memoryless processes. Thanks!
A stochastic process with memory is a type of random process in which the future states of the process depend not only on the current state, but also on the past states. This means that the process has memory or remembers its previous states, unlike a Markov process where the future states only depend on the current state.
In a Markov process, the future states of the process only depend on the current state, whereas in a stochastic process with memory, the future states depend on both the current state and the previous states. This means that a Markov process is memoryless, while a stochastic process with memory has memory.
Stochastic processes with memory have various applications in fields such as finance, physics, biology, and engineering. Some examples include stock market modeling, climate modeling, population growth modeling, and communication networks.
Some common types of stochastic processes with memory include autoregressive processes, moving average processes, and autoregressive moving average (ARMA) processes. These models are often used in time series analysis to predict future values based on past data.
Stochastic processes with memory are studied through mathematical analysis and simulations. Statistical methods such as maximum likelihood estimation and Bayesian inference are commonly used to estimate the parameters of these processes and make predictions about future states.