A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS

Document Type: Other

Author

Abstract

A random walk on a lattice is one of the most fundamental models in probability theory.
When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a
random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT),
and the large deviation principle (LDP) are not fully understood for RWRE. Some known results in the case of LLN and LDP are reviewed.
These results are closely related to the homogenization phenomenon
for Hamilton-Jacobi-Bellman equations when both space and time are discretized.

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History

• Receive Date: 26 May 2009
• Revise Date: 15 December 2009
• Accept Date: 27 December 2009