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Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness .
Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of the classical notion of independence , and it is connected with free products .
The Wiener process is widely considered the most studied and central stochastic process in probability theory. [1] [2] [3] In probability theory and related fields, a stochastic (/ s t ə ˈ k æ s t ɪ k /) or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the ...
In probability theory, a random measure is a measure-valued random element. [ 1 ] [ 2 ] Random measures are for example used in the theory of random processes , where they form many important point processes such as Poisson point processes and Cox processes .
The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a random variable is defined as a measurable function from a probability measure space (called the sample space) to a measurable space.
The Drunkard's Walk discusses the role of randomness in everyday events, and the cognitive biases that lead people to misinterpret random events and stochastic processes. The title refers to a certain type of random walk, a mathematical process in which one or more variables change value under a series of random steps.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
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