8,023 research outputs found
Fock factorizations, and decompositions of the spaces over general Levy processes
We explicitly construct and study an isometry between the spaces of square
integrable functionals of an arbitrary Levy process and a vector-valued
Gaussian white noise. In particular, we obtain explicit formulas for this
isometry at the level of multiplicative functionals and at the level of
orthogonal decompositions, as well as find its kernel. We consider in detail
the central special case: the isometry between the spaces over a Poisson
process and the corresponding white noise. The key role in our considerations
is played by the notion of measure and Hilbert factorizations and related
notions of multiplicative and additive functionals and logarithm. The obtained
results allow us to introduce a canonical Fock structure (an analogue of the
Wiener--Ito decomposition) in the space over an arbitrary Levy process.
An application to the representation theory of current groups is considered. An
example of a non-Fock factorization is given.Comment: 35 pages; LaTeX; to appear in Russian Math. Survey
Sub-additive ergodic theorems for countable amenable groups
In this paper we generalize Kingman's sub-additive ergodic theorem to a large
class of infinite countable discrete amenable group actions.Comment: Journal of Functional Analysi
Stochastic stability at the boundary of expanding maps
We consider endomorphisms of a compact manifold which are expanding except
for a finite number of points and prove the existence and uniqueness of a
physical measure and its stochastical stability. We also characterize the
zero-noise limit measures for a model of the intermittent map and obtain
stochastic stability for some values of the parameter. The physical measures
are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy
Formula
Absolutely Continuous Compensators
We give sufficient conditions on the underlying filtration such that all
totally inaccessible stopping times have compensators which are absolutely
continuous. If a semimartingale, strong Markov process X has a representation
as a solution of a stochastic differential equation driven by a Wiener process,
Lebesgue measure, and a Poisson random measure, then all compensators of
totally inaccessible stopping times are absolutely continuous with respect to
the minimal filtration generated by X. However Cinlar and Jacod have shown that
all semimartingale strong Markov processes, up to a change of time and space,
have such a representation
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