Characterization of probability distributions involves identifying the specific properties or features that define a particular statistical distribution. These characteristics provide a way to distinguish one distribution from another and can also help in the estimation or inference of the underlying random variables. Here are some fundamental aspects involved in the characterization of probability distributions: 1. **Moments**: Moments are expected values of powers of a random variable.
Theorems regarding stochastic processes are mathematical results that describe the behavior, properties, and characteristics of stochastic processes, which are systems that evolve over time with randomness. Here are some important theorems and concepts in the study of stochastic processes: 1. **Markov Property**: A stochastic process satisfies the Markov property if the future state of the process depends only on the present state and not on the past states.