On the Trackability of Stochastic Processes

Abstract

We consider the problem of tracking an unstable stochastic process $X_t$ by using causal knowledge of another stochastic process $Y_t$. We obtain necessary conditions and sufficient conditions for maintaining a finite tracking error. We provide necessary conditions as well as sufficient conditions for the success of this estimation, which is defined as order $m$ moment trackability. By-products of this study are connections between statistics such as R\'{e}nyi entropy, Gallager's reliability function, and the concept of anytime capacity.