Abstract
let us assume that the structure does not change with time. Then the Dow Jones average, as a function of time, is the output of a stationary stochastic process: A sequence X= ... X_2X_1X0X1 .. of real-valued random variables, each a map1 from some underlying probability space to DR. Write P(X0 E [341, 367]) to indicate the probability that today (time zero) the Dow Jones average is between 341 and 367; the function A -) P(XO E A) is the distribution of XO. The process is stationary if the joint distributions are independent of time: For any finite list A 1, .. ., AK of subsets of R, the probability P((Xn+l E Al) & (Xn+2 E A2) &... & (Xn+K E AK)) is independent of n. Henceforth, all processes are assumed to be stationary. An example of a stationary process is a roulette wheel: The next spin produces a number according to the same distribution as the last spin. And each spin is independent of all previous (and all succeeding) spins. Such a process X is called a Bernoulli process: Each random variable Xn has the same distribution as XO, and
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
