Random Probability Measures on Polish Spaces
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a-algebra
A01=Hans Crauel
advanced random measure analysis
Author_Hans Crauel
borel
Borel A-algebra
Bounded Lipschitz Functions
Category=PBK
Category=PBT
Closed Random Set
compact
Compact Random Set
CONDITIONAL EXPECTATION
continuous
Continuous RDS
convergence in law
Dense
dynamical
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Ergodic Invariant Measure
ergodic theory
function
invariant
Invariant Measures
Locally Convex Topological Vector Space
Markov Measure
Measurable Subsets
measure theory
metric
Metric Space
Parabolic Stochastic Partial Differential Equations
Polish Space
probability theory
Prohorov Theorem
Projection Theorem
Random Continuous Function
Random Dynamical System
Random Measure
Random Probability Measures
Random Set
Separable Metric Space
set
Skew Product Flow
stochastic processes
system
topological vector spaces
Universally Complete
Product details
- ISBN 9780367395995
- Weight: 250g
- Dimensions: 156 x 234mm
- Publication Date: 05 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is shown that the topology of convergence in law-which relates to the "statistical equilibrium"-and the narrow topology are incompatible. A brief section on random sets on Polish spaces provides the fundamentals of this theory. In a final section, the results are applied to random dynamical systems to obtain existence results for invariant measures on compact random sets, as well as uniformity results in the individual ergodic theorem. This clear and incisive volume is useful for graduate students and researchers in mathematical analysis and its applications.
Crauel, Hans
