Concepts inStationarity detection in the initial transient problem
Stochastic process
In probability theory, a stochastic process, or sometimes random process (widely used) is a collection of random variables; this is often used to represent the evolution of some random value, or system, over time. This is the probabilistic counterpart to a deterministic process.
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Countable set
In mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor. The elements of a countable set can be counted one at a timeâ€”although the counting may never finish, every element of the set will eventually be associated with a natural number. Some authors use countable set to mean a set with the same cardinality as the set of natural numbers.
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Markov process
In probability theory and statistics, a Markov process, named for the Russian mathematician Andrey Markov, is a stochastic process satisfying a certain property, called the Markov property. A Markov process can be thought of as 'memoryless': loosely speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history. I.e.
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Stationary process
In the mathematical sciences, a stationary process (or strict stationary process or strong stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time or space. Consequently, parameters such as the mean and variance, if they exist, also do not change over time or position.
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Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes.
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Tilde
The tilde is a grapheme with several uses. The name of the character comes from Portuguese and Spanish, from the Latin titulus meaning "title" or "superscription", though the term "tilde" has evolved and now has a different meaning in linguistics. It was originally written over a letter as a mark of abbreviation, but has since acquired a number of other uses as a diacritic mark or a character in its own right.
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Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values. For a more precise definition one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value: when throwing a die, each of the six values 1 to 6 has the probability 1/6.
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Monte Carlo method
Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems. These methods are most suited to calculation by a computer and tend to be used when it is infeasible to compute an exact result with a deterministic algorithm. This method is also used to complement theoretical derivations.
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