Chapter 2 - Limit theorems for dynamic random walks

Abstract

This chapter focuses on the limit theorems for dynamic random walks. The convergence of the finite dimensional distributions can be obtained in a in a classical way. A dynamic random walk can be generated by a dynamical system. Some of the dynamical system can be uniquely ergodic. Behavior of some of the functions obtained by linear interpolation of the values can be used for investigation. A strong law of large numbers for the dynamic random walks can be obtained from Kolmogorov's theorem. This theorem proves that some of the functions can be measured in a specific way. A sequence of random variables can be defined on a probability space. A large deviation principle depends on a good rate function. The random vectors are always independent and can be defined in a specific way. With the help of the contraction principle, a large deviation principle for the random vectors can be derived. The dynamic random walk is more concentrated around the vector null than the simple one.