For times , the corresponding finite-dimensional distribution of a stochastic process is the joint probability distribution of the random vector . The collection of these distributions records every finite set of coordinates of the process.
Articles by others on the same topic
Finite-dimensional distributions are a fundamental concept in probability theory and statistics, particularly in the study of stochastic processes and random variables. In essence, a finite-dimensional distribution refers to the joint distribution of a finite number of random variables. For example, if \(X_1, X_2, \dots, X_n\) are random variables, the finite-dimensional distribution is concerned with the distribution of the vector \((X_1, X_2, \ldots, X_n)\).