Donsker-Varadhan Theorem

The Donsker-Varadhan Theorem is a fundamental result in probability theory that characterizes how likely it is for a stochastic process (a sequence of random events) to deviate from its typical behavior. It provides a way to quantify the "cost" associated with rare events by linking the probability of deviation to a mathematical quantity called the relative entropy or divergence. Essentially, it helps us understand the exponential decay of the probability of large deviations, offering a powerful tool for analyzing the behavior and rare fluctuations of complex stochastic systems.