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31.
José F. Cariñena Manuel F. Rañada 《Journal of Mathematical Analysis and Applications》2007,332(2):975-988
Given a smooth vector field Γ and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that Γ is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction. 相似文献
32.
We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals. 相似文献
33.
Some Results behind Dividend Problems 总被引:1,自引:0,他引:1
Ming Zhou Li Wei Jun-yi Guo 《应用数学学报(英文版)》2006,22(4):681-686
We consider the basic dividend problem of the compound Poisson model with constant barrierstrategy.Some results concealed behind the dividend problem are made explicit in the present work.Differentmethods and some of which are firstly given in this paper.All these results presented certain direct relationshipbetween some important actuary variables in classical risk theory is also revealed. 相似文献
34.
The purpose of this paper is two-fold. First, we introduce a new asymptotic expansion in the exponent for the compound binomial
approximation of the generalized Poisson binomial distribution. The dependence of its accuracy on the symmetry and shifting
of distributions is investigated. Second, for compound binomial and compound Poisson distributions, we present new smoothness
estimates, some of which contain explicit constants. Finally, the ideas used in this paper enable us to prove new precise
bounds in the compound Poisson approximation.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 1, pp. 67–110, January–March, 2006. 相似文献
35.
Suppose there is a Poisson process of points X
i
on the line. Starting at time zero, a grain begins to grow from each point X
i
, growing at rate A
i
to the left and rate B
i
to the right, with the pairs (A
i
, B
i
) being i.i.d. A grain stops growing as soon as it touches another grain. When all growth stops, the line consists of covered intervals (made up of contiguous grains) separated by gaps. We show (i) a fraction 1/e of the line remains uncovered, (ii) the fraction of covered intervals which contain exactly k grains is (k–1)/k!, (iii) the length of a covered interval containing k grains has a gamma(k–1) distribution, (iv) the distribution of the grain sizes depends only on the distribution of the total growth rate A
i
+B
i
, and other results. Similar theorems are obtained for growth processes on a circle; in this case we need only assume the pairs (A
i
, B
i
) are exchangeable. These results extend those of Daley, et al. (2000) who studied the case where A
i
=B
i
=1. Simulation results are given to illustrate the various theorems. 相似文献
36.
37.
The paper is devoted to the research of large deviation probabilities in the approximation by compound Poisson law. 相似文献
38.
We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature. 相似文献
39.
40.
Richard Arratia Bla Bollobs Gregory B. Sorkin 《Journal of Combinatorial Theory, Series B》2004,92(2):199-233
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers. 相似文献