Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

Design of recursive least-squares fixed-lag smoother using covariance information in linear continuous stochastic systems

This paper newly designs the recursive least-squares (RLS) fixed-lag smoother and filter using the covariance information in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The estimators require the covariance information of the signal and the variance of the observation noise. The auto-covariance function of the signal is expressed in the semi-degenerate kernel form.     

Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Designing a majorization scheme for the recourse function in two-stage stochastic linear programming

We discuss issues pertaining to the domination from above of the second-stage recourse function of a stochastic linear program and we present a scheme to majorize this function using a simpler sublinear function. This majorization is constructed using special geometrical attributes of the recourse function. The result is a proper, simplicial function with a simple characterization which is well-suited for calculations of its expectation as required in the computation of stochastic programs. Experiments indicate that the majorizing function is well-behaved and stable.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

Hamiltonian formulation of generalized quantum dynamics

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations. Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.