2016 / September Volume 11 No.3
Weak Convergence of Probability Measures on Metric Spaces of Nonlinear Operators
| Published Date |
2016 / September
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|---|---|
| Title | Weak Convergence of Probability Measures on Metric Spaces of Nonlinear Operators |
| Author | |
| Keyword | |
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| Pagination | 485-519 |
| Abstract | The conditions for weak convergence of a sequence of probability measures on metric spaces of nonlinear
operators defined on some subsets of a real separable Banach space are established.
The nonlinear operators of interest include either continuous operators or
cadlag (continu $\grave{a}$ droite,
limites $\grave{a}$ gauche) operators defined in this article.
As the domains of the operators are
certain compact sets, the limiting probability measures are the generalizations of
the Wiener measure and the Poisson measure on the metric spaces of
continuous and cadlag real functions defined on the unit interval,
respectively. As
the limiting probability measure is the generalized Wiener measure, the result is
a generalization of Donsker's theorem.
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| DOI | |
| AMS Subject Classification |
60F17, 60F05
|
| Received |
2016-07-25
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| Accepted |
2016-07-17
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