Consider the stochastic processes X1, X2,... and Λ1, Λ2,... where the X process can be thought of as observations on the Λ process. We investigate the asymptotic behavior of the conditional distributions of Xt+v given X1,..., Xt and Λt+v given X1,..., Xt with regard to their dependency on the "early" part of the X process. These distributions arise in various time series and sequential decision theory problems. The results support the intuitively reasonable and often used (as a basic tenet of model building) assumption that only the more recent past is needed for near optimal prediction.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Markov process
- Stochastic process
- stationary process