Stochastic process
A Stochastic process is a mathematical description of random events that occur one after another.[1] It is possible to order these events according to the time at which they occur.
This can be used to model such things as daily weather data, or exchange rate changes, or medical information like a patient's EKG, EEG, blood pressure or temperature.[1]
Stochastic processes used in various disciplines, including physics, biology, finance, telecommunications, and operations research.They provide a powerful framework for analyzing and predicting the behavior of systems under uncertain conditions.
Stochastic Process Media
A computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.
A single computer-simulated sample function or realization, among other terms, of a three-dimensional Wiener or Brownian motion process for time 0 ≤ t ≤ 2. The index set of this stochastic process is the non-negative numbers, while its state space is three-dimensional Euclidean space.
Realizations of Wiener processes (or Brownian motion processes) with drift (blue) and without drift (red)
Mathematician Joseph Doob did early work on the theory of stochastic processes, making fundamental contributions, particularly in the theory of martingales. His book Stochastic Processes is considered highly influential in the field of probability theory.
Norbert Wiener gave the first mathematical proof of the existence of the Wiener process. This mathematical object had appeared previously in the work of Thorvald Thiele, Louis Bachelier, and Albert Einstein.
References
- ↑ 1.0 1.1 "Stochastic process". princeton.edu. 2014. Archived from the original on 4 October 2014. Retrieved 18 January 2015.