“stochastic process”的概念、定义、翻译、参考文献-科学参考

stochastic process

Physics

Any process in which there is a random element. Stochastic processes are important in nonequilibrium statistical mechanics and disordered solids. In a time-dependent stochastic process, a variable that changes with time does so in such a way that there is no correlation between different time intervals. An example of a stochastic process is Brownian movement. Equations, such as the Langevin equation and the Fokker–Planck equation, that describe stochastic processes are called stochastic equations. It is necessary to use statistical methods and the theory of probability to analyse stochastic processes and their equations.

Mathematics

A family {X(t), t ε‎ T} of random variables, where T is some index set. Often the index set is the set ℕ of natural numbers, and the stochastic process is a sequence X₁, X₂, X₃,…of random variables. For example, X_n may be the outcome of the nth trial of some experiment, or the nth in a set of observations. The possible values taken by the random variables are often called states, and these form the state space. The state space is said to be discrete if it is countable, and continuous if it is uncountable. See Markov chain, Poisson process.

Statistics

A finite collection of related random variables, often ordered in time or space. The possible values of a random variable are referred to as states and the possible configurations of the states of all the random variables constitute the state space. Examples of stochastic processes include Brownian motion, the counting process, the Markov chain (see Markov process), the Poisson process, and the random walk. The phrase ‘stochastic process’ was used by Kolmogorov in 1932.

Chemistry

Any process in which there is a random element. Stochastic processes are important in nonequilibrium statistical mechanics and disordered solids. In a time-dependent stochastic process, a variable that changes with time does so in such a way that there is no correlation between different time intervals. An example of a stochastic process is Brownian movement. Equations, such as the Langevin equation and the Fokker–Planck equation, that describe stochastic processes are called stochastic equations. It is necessary to use statistical methods and the theory of probability to analyse stochastic processes and their equations.

Chemical Engineering

A statistical way of generating a series of random values of a mathematical variable and building up a particular statistical distribution from these values. Stochastic processes are used in non-equilibrium statistical mechanics.

Computer

A set of random variables whose values vary with time (or sometimes in space). Examples include populations affected by births and deaths, the length of a queue (see queuing theory), or the amount of water in a reservoir. Stochastic models are models in which random variation is of major importance, in contrast to deterministic models. Stochastic processes give theoretical explanations for many probability distributions, and underlie the analysis of time series data.

Electronics and Electrical Engineering

Any process in which there is a random element.

Philosophy

A process characterized by the values taken by a set of random variables whose values change with time. Standard examples include the length of a queue, where there is a probability of someone leaving or entering in a given interval of time, but the actual events of people leaving and entering are randomly distributed; or the size of a population, or the quantity of water in a reservoir.

Economics

A family, or a collection of random variables, indexed by time. It is said to be a discrete process, or a discrete time process, if the time index only takes integer values (typically, 0,±1,±2,…), and a continuous process, or a continuous time process, if the time index takes a continuous range of real values (finite or infinite).

单词	stochastic process
释义	stochastic process Physics Any process in which there is a random element. Stochastic processes are important in nonequilibrium statistical mechanics and disordered solids. In a time-dependent stochastic process, a variable that changes with time does so in such a way that there is no correlation between different time intervals. An example of a stochastic process is Brownian movement. Equations, such as the Langevin equation and the Fokker–Planck equation, that describe stochastic processes are called stochastic equations. It is necessary to use statistical methods and the theory of probability to analyse stochastic processes and their equations. Mathematics A family {X(t), t ε‎ T} of random variables, where T is some index set. Often the index set is the set ℕ of natural numbers, and the stochastic process is a sequence X₁, X₂, X₃,…of random variables. For example, X_n may be the outcome of the nth trial of some experiment, or the nth in a set of observations. The possible values taken by the random variables are often called states, and these form the state space. The state space is said to be discrete if it is countable, and continuous if it is uncountable. See Markov chain, Poisson process. Statistics A finite collection of related random variables, often ordered in time or space. The possible values of a random variable are referred to as states and the possible configurations of the states of all the random variables constitute the state space. Examples of stochastic processes include Brownian motion, the counting process, the Markov chain (see Markov process), the Poisson process, and the random walk. The phrase ‘stochastic process’ was used by Kolmogorov in 1932. Chemistry Any process in which there is a random element. Stochastic processes are important in nonequilibrium statistical mechanics and disordered solids. In a time-dependent stochastic process, a variable that changes with time does so in such a way that there is no correlation between different time intervals. An example of a stochastic process is Brownian movement. Equations, such as the Langevin equation and the Fokker–Planck equation, that describe stochastic processes are called stochastic equations. It is necessary to use statistical methods and the theory of probability to analyse stochastic processes and their equations. Chemical Engineering A statistical way of generating a series of random values of a mathematical variable and building up a particular statistical distribution from these values. Stochastic processes are used in non-equilibrium statistical mechanics. Computer A set of random variables whose values vary with time (or sometimes in space). Examples include populations affected by births and deaths, the length of a queue (see queuing theory), or the amount of water in a reservoir. Stochastic models are models in which random variation is of major importance, in contrast to deterministic models. Stochastic processes give theoretical explanations for many probability distributions, and underlie the analysis of time series data. Electronics and Electrical Engineering Any process in which there is a random element. Philosophy A process characterized by the values taken by a set of random variables whose values change with time. Standard examples include the length of a queue, where there is a probability of someone leaving or entering in a given interval of time, but the actual events of people leaving and entering are randomly distributed; or the size of a population, or the quantity of water in a reservoir. Economics A family, or a collection of random variables, indexed by time. It is said to be a discrete process, or a discrete time process, if the time index only takes integer values (typically, 0,±1,±2,…), and a continuous process, or a continuous time process, if the time index takes a continuous range of real values (finite or infinite).
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