Date of Award
Master of Science (MS)
Mathematics and Statistics
Michael P. Weill
Differential equations have been used to model physical systems, but in many processes this has not been sufficient due to the presence of random occurrences in the system. One method of dealing with this problem is to model the system as a stochastic or random process.
A stochastic process, x, is a function mapping the product of a probability space, Ω, and a subset of the real numbers, TcR, into the real numbers, x: Ω*T→R. In many physical situations, T can be thought of as representing time and Ω as all possible outcomes of the process. For a fixed t ∈T, xt(·) is a random variable, and for a fixed ωƐΩ, x (ω) is called a sample function for the stochastic process. (For notational convenience, a stochastic process xt(ω) will be denoted by xt, the outcome, ω, being understood.)
Knipfer, Diane, "Stochastic Integration" (1977). All Graduate Plan B and other Reports. 1172.