8/12/2023 0 Comments Stochastic methodsBecause of its randomness, a stochastic process can have many outcomes, and a single outcome of a stochastic process is known as, among other things, a sample function or realization.Ī stochastic process can be classified in a variety of ways, such as by its state space, index set, or the dependence among random variables and stochastic processes are classified in a single way, the cardinality of the index set and the state space. A stochastic process's increment is the amount that a stochastic process changes between two index values, which are frequently interpreted as two points in time. This state-space could be the integers, the real line, or η-dimensional Euclidean space, for example. Įach random variable in the collection of the values is taken from the same mathematical space, known as the state space. Stochastic Process Meaning is one that has a system for which there are observations at certain times, and that the outcome, that is, the observed value at each time is a random variable. The index set was traditionally a subset of the real line, such as the natural numbers, which provided the index set with time interpretation. The index set is the set used to index the random variables. Each probability and random process are uniquely associated with an element in the set. A stochastic process, also known as a random process, is a collection of random variables that are indexed by some mathematical set.
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