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Markov processes are stochastic processes, traditionally in discrete or continuous time, that have the Markov property, which means the next value of the Markov process depends on the current value, but it is conditionally independent of the previous values of the stochastic process. In other words, the behavior of the process in the future is ...
2.1 In probability and stochastic processes. ... Download as PDF; Printable version; ... Chinese restaurant process;
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is ...
In the theory of stochastic processes, a subdiscipline of probability theory, filtrations are totally ordered collections of subsets that are used to model the information that is available at a given point and therefore play an important role in the formalization of random (stochastic) processes.
A Markov chain with two states, A and E. In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past.
Consider a probability space (Ω, Σ, P) and suppose that the (random) state Y t in n-dimensional Euclidean space R n of a system of interest at time t is a random variable Y t : Ω → R n given by the solution to an Itō stochastic differential equation of the form
In many real world applications, a first-hitting-time (FHT) model has three underlying components: (1) a parent stochastic process {()}, which might be latent, (2) a threshold (or the barrier) and (3) a time scale. The first hitting time is defined as the time when the stochastic process first reaches the threshold.