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Mathematical Foundations of the State Lumping of Large Systems (Paperback, Softcover reprint of the original 1st ed. 1993)
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Mathematical Foundations of the State Lumping of Large Systems (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Mathematics and Its Applications, 264
Expected to ship within 10 - 15 working days
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During the investigation of large systems described by evolution
equations, we encounter many problems. Of special interest is the
problem of "high dimensionality" or, more precisely, the problem of
the complexity of the phase space. The notion of the "comple xity
of the. phase space" includes not only the high dimensionality of,
say, a system of linear equations which appear in the mathematical
model of the system (in the case when the phase space of the model
is finite but very large), as this is usually understood, but also
the structure of the phase space itself, which can be a finite,
countable, continual, or, in general, arbitrary set equipped with
the structure of a measurable space. Certainly, 6 6 this does not
mean that, for example, the space (R 6, ( ), where 6 is a a-algebra
of Borel sets in R 6, considered as a phase space of, say, a
six-dimensional Wiener process (see Gikhman and Skorokhod [1]), has
a "complex structure". But this will be true if the 6 same space (R
6, ( ) is regarded as a phase space of an evolution system
describing, for example, the motion of a particle with small mass
in a viscous liquid (see Chandrasek har [1]).
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