These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries. Erlang to study the number of phone calls occurring in a certain period of time. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. Īpplications and the study of phenomena have in turn inspired the proposal of new stochastic processes.
Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner.
In probability theory and related fields, a stochastic ( / s t oʊ ˈ k æ s t ɪ k/) or random process is a mathematical object usually defined as a family of random variables. The Wiener process is widely considered the most studied and central stochastic process in probability theory. A computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere.