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Stochastic forensics analyzes computer crime by viewing computers as stochastic steps. In artificial intelligence , stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing , stochastic neural networks , stochastic optimization , genetic algorithms , and genetic programming .
Martingales can also be created from stochastic processes by applying some suitable transformations, which is the case for the homogeneous Poisson process (on the real line) resulting in a martingale called the compensated Poisson process. [209] Martingales can also be built from other martingales. [212]
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created and started by the Japanese mathematician Kiyosi Itô during World War II.
The theory of stochastic processes broadened into such areas as Markov processes and Brownian motion, the random movement of tiny particles suspended in a fluid. That provided a model for the study of random fluctuations in stock markets, leading to the use of sophisticated probability models in mathematical finance , including such successes ...
Along with providing better understanding and unification of discrete and continuous probabilities, measure-theoretic treatment also allows us to work on probabilities outside , as in the theory of stochastic processes. For example, to study Brownian motion, probability is defined on a space of functions.
Stochastic oscillator is a momentum indicator within technical analysis that uses support and resistance levels as an oscillator. George Lane developed this indicator in the late 1950s. [ 1 ] The term stochastic refers to the point of a current price in relation to its price range over a period of time. [ 2 ]
Louis Jean-Baptiste Alphonse Bachelier (French:; 11 March 1870 – 28 April 1946) [1] was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, as part of his doctoral thesis The Theory of Speculation (Théorie de la spéculation, defended in 1900).
Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed by simple bit-wise operations on the streams. Complex computations can then be computed by simple bit-wise operations on the streams.