Concepts inStationarity detection in the initial transient problem
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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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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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 time¿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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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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Regenerative process
In applied probability, a regenerative process is a special type of stochastic process that is defined by having a property whereby certain portions of the process can be treated as being statistically independent of each other. This property can be used in the derivation of theoretical properties of such processes.
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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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Asterisk
An asterisk is a typographical symbol or glyph. It is so called because it resembles a conventional image of a star. Computer scientists and mathematicians often pronounce it as star (as, for example, in the A* search algorithm or C*-algebra). In English, an asterisk is usually five-pointed in sans-serif typefaces, six-pointed in serif typefaces, and six- or eight-pointed when handwritten. It can be used to censor vulgar words or objectionable text.
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