3,915 research outputs found
ITERATED -FRACTIONAL VECTOR REPRESENTATION FORMULAE AND INEQUALITIES FOR BANACH SPACE VALUED FUNCTIONS
Here we present very general iterated fractional
Bochner integral representation formulae for Banach space valued functions. Based on these we derive generalized and iterated left and right: fractional Poincar´e type inequalities, fractional Opial type inequalities and fractional Hilbert-Pachpatte inequalities. All these inequalities are very general having in their background Bochner type integrals
Parafermionic quasi-particle basis and fermionic-type characters
A new basis of states for highest-weight modules in \ZZ_k parafermionic
conformal theories is displayed. It is formulated in terms of an effective
exclusion principle constraining strings of fundamental parafermionic
modes. The states of a module are then built by a simple filling process, with
no singular-vector subtractions. That results in fermionic-sum representations
of the characters, which are exactly the Lepowsky-Primc expressions. We also
stress that the underlying combinatorics -- which is the one pertaining to the
Andrews-Gordon identities -- has a remarkably natural parafermionic
interpretation.Comment: minor modifications and proof in app. C completed; 34 pages (harvmac
b
Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion
For stochastic differential equation driven by fractional Brownian motion
with Hurst parameter , Harnack type inequalities are established by
constructing a coupling with unbounded time-dependent drift. These inequalities
are applied to the study of existence and uniqueness of invariant measure for a
discrete Markov semigroup constructed in terms of the distribution of the
solution. Furthermore, we show that entropy-cost inequality holds for the
invariant measure
Integral equations PS-3 and moduli of pants
More than a hundred years ago H.Poincare and V.A.Steklov considered a problem
for the Laplace equation with spectral parameter in the boundary conditions.
Today similar problems for two adjacent domains with the spectral parameter in
the conditions on the common boundary of the domains arises in a variety of
situations: in justification and optimization of domain decomposition method,
simple 2D models of oil extraction, (thermo)conductivity of composite
materials. Singular 1D integral Poincare-Steklov equation with spectral
parameter naturally emerges after reducing this 2D problem to the common
boundary of the domains. We present a constructive representation for the
eigenvalues and eigenfunctions of this integral equation in terms of moduli of
explicitly constructed pants, one of the simplest Riemann surfaces with
boundary. Essentially the solution of integral equation is reduced to the
solution of three transcendent equations with three unknown numbers, moduli of
pants. The discreet spectrum of the equation is related to certain surgery
procedure ('grafting') invented by B.Maskit (1969), D.Hejhal (1975) and
D.Sullivan- W.Thurston (1983).Comment: 27 pages, 13 figure
Representation formulae for the fractional Brownian motion
We discuss the relationships between some classical representations of the
fractional Brownian motion, as a stochastic integral with respect to a standard
Brownian motion, or as a series of functions with independent Gaussian
coefficients. The basic notions of fractional calculus which are needed for the
study are introduced. As an application, we also prove some properties of the
Cameron-Martin space of the fractional Brownian motion, and compare its law
with the law of some of its variants. Several of the results which are given
here are not new; our aim is to provide a unified treatment of some previous
literature, and to give alternative proofs and additional results; we also try
to be as self-contained as possible.Comment: to appear in "S\'eminaire de Probabilit\'es
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