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Random Processes in Physics and Finance$
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Melvin Lax, Wei Cai, and Min Xu

Print publication date: 2006

Print ISBN-13: 9780198567769

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567769.001.0001

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What is a random process

What is a random process

Chapter:
(p.44) 2 What is a random process
Source:
Random Processes in Physics and Finance
Author(s):

Melvin Lax

Wei Cai

Min Xu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567769.003.0002

A random or stochastic process is a random variable that evolves in time by some random mechanism (of course, the time variable can be replaced by a space variable, or some other variable, in application). The variable can have a discrete set of values at a given time, or a continuum of values may be available. Likewise, the time variable can be discrete or continuous. A stochastic process is regarded as completely described if the probability distribution is known for all possible sets of times. A stationary process is one which has no absolute time origin. All probabilities are independent of a shift in the origin of time. This chapter discusses multitime probability description, conditional probabilities, stationary, Gaussian, and Markovian processes, and the Chapman–Kolmogorov condition.

Keywords:   random process, stochastic process, time variable, probability distribution, multitime probability description, conditional probabilities, stationary process, Gaussian process, Markovian process, Chapman–Kolmogorov condition

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