2014 We establish classically the probability distribution (P-distribution) for the complex amplitudes of multimodal and unimodal optical fields belonging to the class of generalized Gaussian fields recently introduced. From this result follows immediately the unique P-representation for this class of fields. However, all the generalized Gaussian fields, except the chaotic field, are not fully ...

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptot...

We construct a stationary ergodic process {X1, X2, X3 . . .} such that each Xt, 1 ≤ t <∞, has the uniform distribution on the unit square and the length Ln of the shortest path through {X1, X2, . . . , Xn} is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton and Hammersley theorem does not extend from the case of independent uniformly di...

With the development of network technology and growing enlargement of network size, the network structure is becoming more and more complicated. Mutual interactions of different network equipment, topology configurations, transmission protocols and cooperation and competition among the network users inevitably cause the network traffic flow which is controlled by several driving factors to appe...

The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Lévy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density function of Lévy flights in different smooth potential profiles. We find confinement of the particle in the superdiffusion motion with a bimodal stationary ...

In this paper we derive the canonical distribution as a stationary solution of the Liouville equation for the classical dissipative system. Dissipative classical systems can have stationary states look like canonical Gibbs distributions. The condition for non-potential forces which leads to this stationary solution is very simple: the power of the non-potential forces must be directly proportio...

In a first part, we prove a Lyapunov-type criterion for the ξ1-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on...

Abstract. A system of globally coupled rotors is studied in a unified framework of microcanonical and canonical ensembles. We consider the Fokker-Planck equation governing the time evolution of the system, and examine various stationary as well as non-stationary solutions. The canonical distribution, describing equilibrium, provides a stationary solution also in the microcanonical ensemble, whi...

In this paper we study a Geo/T-IPH/1 queue model, where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states. The queue model can be described by a quasi-birth-anddeath (QBD) process with countably phases. Using the operator-geometric solution method, we first give the expression of the operator and the joint stationary distribu...

We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.