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LvyProcesses--From ProbabilitytoFinance
 

Summary: LÚvyProcesses--From
ProbabilitytoFinance
andQuantumGroups
David Applebaum
1320 NOTICES OF THE AMS VOLUME 51, NUMBER 11
T
he theory of stochastic processes was
one of the most important mathematical
developments of the twentieth century.
Intuitively, it aims to model the interac-
tion of "chance" with "time". The tools
with which this is made precise were provided by
the great Russian mathematician A. N. Kolmogorov
in the 1930s. He realized that probability can be
rigorously founded on measure theory, and then
a stochastic process is a family of random variables
(X(t), t 0) defined on a probability space (, F, P)
and taking values in a measurable space (E, E).
Here is a set (the sample space of possible out-
comes), F is a -algebra of subsets of (the events),

  

Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield

 

Collections: Mathematics