Products of Beta matrices and sticky flows

A discrete model of Brownian sticky flows on the unit circle is described: it is constructed with products of Beta matrices on the discrete torus. Sticky flows are defined by their moments which are consistent systems of transition kernels on the unit circle. Similarly, the moments of the discrete model form a consistent system of transition matrices on the discrete torus. A convergence of Beta matrices to sticky kernels is shown at the level of the moments. As the generators of the n-point processes are defined in terms of Dirichlet forms, the proof is performed at the level of the Dirichlet forms. The evolution of a probability measure by the flow of Beta matrices is described by a measure-valued Markov process. A convergence result of its finite dimensional distributions is deduced.Mathematics Subject Classification (2000):60J27, 60J35, 60G09     

Proper extensions of weakly left ample semigroups

Summary We consider proper (idempotent pure) extensions of weakly left ample semigroups. These are extensions that are injective in each <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\widetilde{\mathcal{R}}$-class. A graph expansion of a weakly left ample semigroup S is shown to be such an extension of S. Using semigroupoids acted upon by weakly left ample semigroups, we prove that any weakly left ample semigroup which is a proper extension of another such semigroup T is (2,1)-embeddable into a λ-semidirect product of a semilattice by T. Some known results, by O'Carroll, for idempotent pure extensions of inverse semigroups and, by Billhardt, for proper extensions of left ample semigroups follow from this more general situation.     

Approximation methods for nonlinear operator equations

Let be a real normed linear space and be a uniformly quasi-accretive map. For arbitrary define the sequence by where is a positve real sequence satisfying the following conditions: (i) ; (ii) . For , assume that 0$"> and that , where (the set of all positive integers): and is a strictly increasing function with . It is proved that a Mann-type iteration process converges strongly to . Furthermore if, in addition, is a uniformly continuous map, it is proved, without the condition on , that the Mann-type iteration process converges strongly to . As a consequence, corresponding convergence theorems for fixed points of hemi-contractive maps are proved.

     

A New Method for Approximations in Probability and Operator Theories

The aim of this work is to introduce a new approach in normal approximations, approximations of semigroups of operators, and approximations by accompanying laws. We describe the method and provide several examples showing how the method works. Loosely speaking, the approach is based on multiplicative representations of differences to estimate. The method considerably reduces the technical part of proofs compared to the traditional approaches. In probability theory, it nicely applies to the nonidentically distributed case; another advantage of the method is its extendability to the case of dependent random variables.     

Contraction Integrated Semigroups and Their Application to Continuous-time Markov Chains

We introduce the notion of the contraction integrated semigroups and give the Lumer-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.     

The domains of partial attraction of probabilities on groups and on vector spaces

It is shown that for exponential Lie groupsG the limit behavior of i.i.d. triangular arrays on the groupG and on the tangent spaceG coincide. This result is used to obtain a characterization of domains of partial attraction (resp. semistable attraction) on exponential (resp. simply connected nilpotent) Lie groups via the corresponding domains on the tangent space.     

（T＋λI）~（－1）不一定是非扩张映射

设Ｔ是ｍ增生算子，Ｉ是恒等映射．本文通过一个反例说明（Ｔ＋λＩ）－１（λ＞０）不一定是非扩张映射．     

Piecewise deterministic quantum dynamics and quantum fractals on the Poincaré disk

It is shown that piecewise deterministic dissipative quantum dynamics in a vector space withindefinite metric can lead to well defined, positive probabilities. The case of quantum jumps on the Poincar'e disk is studied in detail including results of numerical simulations of quantum fractals.     

Functional Calculus for Infinitesimal Generators of Holomorphic Semigroups

We give a functional calculus formula for infinitesimal generators of holomorphic semigroups of operators on Banach spaces, which involves the Bochner–Riesz kernels of such generators. The rate of smoothness of operating functions is related to the exponent of the growth on vertical lines of the operator norm of the semigroup. The strength of the formula is tested on Poisson and Gauss semigroups inL¹(Rⁿ) andL¹(G), for a stratified Lie groupG. We give also a self-contained theory of smooth absolutely continuous functions on the half line [0, ∞).