Unable to retrieve citations for this document

Retrieving citations for document...

Dmitri L. Finkelshtein, Yuri G. Kondratiev, Eugene W. Lytvynov
June 28, 2007

### Abstract

A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in ℝ d which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure µ as invariant measure. We study a scaling limit of such a dynamics, derived through a scaling of the jump rate. Informally, we expect that, in the limit, only jumps of "infinite length" will survive, i.e., we expect to arrive at a Glauber dynamics in continuum (a birth-and-death process in ℝ d ). We prove that, in the low activity-high temperature regime, the generators of the Kawasaki dynamics converge to the generator of a Glauber dynamics. The convergence is on the set of exponential functions, in the L 2 ( µ )-norm. Furthermore, additionally assuming that the potential of pair interaction is positive, we prove the weak convergence of the finite-dimensional distributions of the processes.

Unable to retrieve citations for this document

Retrieving citations for document...

Wiyada Kumam, Poom Kumam
June 28, 2007

### Abstract

The purpose of this paper is to prove some random fixed point theorem for multivalued nonexpansive non-self random operators. We will prove the existence of a random fixed point theorem for multivalued non-self random operator in the framework of a Banach space with property (D), and satisfying an inwardness condition. Our work also extends the stochastic version of the results of Kumam [P. Kumam, A note on some fixed point theorems for set-valued non-self mappings in Banach spaces. Int. Journal of Math. Analysis, to appear.], and improves the work of Kumam and Plubtieng [P. Kumam and S. Plubtieng, Random fixed point theorems for multivalued nonexpansive operators in uniformly nonsquare Banach spaces. Random Oper. and Stoch. Equ . 14(1) (2006), 35–44.].

Unable to retrieve citations for this document

Retrieving citations for document...

Modeste Nzi, Ibrahima Mendy
June 28, 2007

### Abstract

Under the topology of anisotropic Besov spaces, we prove the convergence in law of a random walk defined by the partial sums of a mean zero stationary Gaussian fields to the fractional Brownian sheet.

Unable to retrieve citations for this document

Retrieving citations for document...

I. V. Evstigneev, S. A. Pirogov
June 28, 2007

### Abstract

We provide conditions for the existence of measurable solutions to the equation ξ( Tω ) = f ( ω , ξ ( ω )), where T : Ω → Ω is an automorphism of the probability space Ω and f ( ω , ·) is a strictly (but not necessarily uniformly) contracting mapping.

Unable to retrieve citations for this document

Retrieving citations for document...

Erika Alejandra Rada-Mora, Daya K. Nagar
June 28, 2007

### Abstract

Let X 1 , ... , X r +1 be independent random variables having a standard gamma distribution with respective shape parameters α 1 , ... , α r +1 and define , i = 1, ... , r and , i = 1, ... , r where a ≠ 0 and b > 0 are constants. Then, ( Y 1 , ... , Y r ) and ( Z 1 , ... , Z r ) follow multivariate generalized beta type 1 and type 2 distributions, respectively. In this article several properties of these distributions are studied.

Unable to retrieve citations for this document

Retrieving citations for document...

R. D. Rodríguez-Said, A. A. Pogorui, R. M. Rodríguez-Dagnino
June 28, 2007

### Abstract

In this paper we study the stationary probability distribution of a system consisting of a finite capacity buffer connected to N equal customers with bursty on-off demands. We assume that the buffer is filled up at a constant rate and we analyze the case when this filling rate satisfies an optimization condition according to the customer demands. First, we consider semi-Markov on-off demands for the case N = 2 and we model the dynamics of the system using a semi-Markov evolution environment. We show that we can use the phase merging algorithm to reduce the problem to a Markov evolution environment case. Then, we generalize the results for any N using a birth-and-death process.