共查询到20条相似文献,搜索用时 31 毫秒
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为了刻画复杂随机系统的理性决策,提出了复杂随机系统的生存性及不变性的概念,给出并证明了复杂随机系统的生存性定理及不变性定理.并提出了均方相依锥,生存域与不变域的概念.得到了与文献中的一致的结论. 相似文献
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相对论Birkhoff系统的形式不变性与Noether守恒量 总被引:2,自引:0,他引:2
研究相对论Birkhoff系统的形式不变性,寻求系统的守恒量。在群的无限小变换下,给出相对论Birkhoff系统的形式不变性的定义和判剧。基于相对论Pfaff-Birkhoff-D'Alembert原理在群的无限小变换下的变形形式,建立相对论Birkhoff系统的Noether对称性理论。通过研究形式不变性与Noether对称性之间的关系,得到相对论Birkhoff系统的守恒量。研究结果表明:在一定的条件下,相对论Birkhoff系统的形式不变性导致Noether对称性的守恒量。 相似文献
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The objective of this paper is to consider shift invariance, a specific type of exchangeability, of random factors in linearmodels.
The randomfactors are described via their covariance matrices and it is shown that shift invariance implies circular Toeplitz
covariancematrices and marginally shift invariance implies block circular Toeplitz covariance matrices. In order to get interpretable
linear models reparametrization is performed. It is shown that by putting restrictions on the spectrum of the shift invariant
covariance matrices natural reparametrization conditions for the corresponding factors are obtained which then, among others,
can be used to obtain unique parametrizations under shift invariance.
相似文献
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强不变原理与完全收敛性的统一形式 总被引:1,自引:0,他引:1
本文建立了强不变原理与完全收效性的统一形式,得到了用强不变原理研究完全收敛性的方法,前人许多关于强不交原理和完全收敛性的结论是本文的推论. 相似文献
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The invariance principles for autonomous difference systems with infinite delay are established.As applications of the obtained invariance principles, criteria for asymptotic stability and asymptotic constancy of solutions are also given. 相似文献
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This paper studies conditions for invariance of dynamical systems on stratified domains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with non-Lipschitz data. This is done via the identification of a new multifunction, the essential velocity multifunction. Properties of this multifunction are investigated and used to establish the relevant invariance criteria. 相似文献
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《随机分析与应用》2013,31(5):955-981
Abstract Thanks to the Stroock and Varadhan “Support Theorem” and under convenient regularity assumptions, stochastic viability problems are equivalent to invariance problems for control systems (also called tychastic viability), as it has been singled out by Doss in 1977 for instance. By the way, it is in this framework of invariance under control systems that problems of stochastic viability in mathematical finance are studied. The Invariance Theorem for control systems characterizes invariance through first‐order tangential and/or normal conditions whereas the stochastic invariance theorem characterizes invariance under second‐order tangential conditions. Doss's Theorem states that these first‐order normal conditions are equivalent to second‐order normal conditions that we expect for invariance under stochastic differential equations for smooth subsets. We extend this result to any subset by defining in an adequate way the concept of contingent curvature of a set and contingent epi‐Hessian of a function, related to the contingent curvature of its epigraph. This allows us to go one step further by characterizing functions the epigraphs of which are invariant under systems of stochastic differential equations. We shall show that they are (generalized) solutions to either a system of first‐order Hamilton‐Jacobi equations or to an equivalent system of second‐order Hamilton‐Jacobi equations. 相似文献
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Guy Martial Nkiet 《Journal of multivariate analysis》2003,84(1):1-18
Using a recent result about the invariance problem in linear canonical analysis (LCA), we introduce a criterion by means of which one can see if this invariance holds when the related random vectors are transformed by linear maps. Then, the estimation of this criterion is considered as well as the problem of testing for invariance of LCA. Particularly, a new test for additional information in canonical analysis is proposed and simulations are used to gain understanding of the finite sample performance of this test and to compare it with the likelihood ratio test. 相似文献
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Hybrid systems with memory are dynamical systems exhibiting both delayed and hybrid dynamics. Such systems can be described by hybrid functional inclusions. Classical invariance principles play an instrumental role in proving stability and convergence of dynamical systems. Invariance principles for general hybrid systems with delays, however, remain an open topic. In this paper, we prove invariance principles for hybrid systems with memory, using both Lyapunov–Razumikhin function and Lyapunov–Krasovskii functional methods. These invariance principles are then applied to derive two stability results as corollaries. 相似文献
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Continuity properties and Trotter's formula for the transition semigroups corresponding to Markov processes are discussed.
Applications to stochastic invariance are given as well. The research was motivated by the semigroup approach to invariance
proposed by P. Kotelenez in [9].
November 15, 1998 相似文献
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Arash Yavari Jerrold E. Marsden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,133(1):723-738
This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles
under groups of transformations. Balance of energy and its invariance is first examined in Euclidean space. Unlike the case
of continuous media, it is shown that conservation and balance laws do not follow from the assumption of invariance of balance of energy under time-dependent isometries of the ambient space. However,
the postulate of invariance of balance of energy under arbitrary diffeomorphisms of the ambient (Euclidean) space, does yield the correct conservation and balance laws.
These ideas are then extended to the case when the ambient space is a Riemannian manifold. Pairwise interactions in the case
of geodesically complete Riemannian ambient manifolds are defined by assuming that the interaction potential explicitly depends
on the pairwise distances of particles. Postulating balance of energy and its invariance under arbitrary time-dependent spatial
diffeomorphisms yields balance of linear momentum. It is seen that pairwise forces are directed along tangents to geodesics
at their end points. One also obtains a discrete version of the Doyle–Ericksen formula, which relates the magnitude of internal
forces to the rate of change of the interatomic energy with respect to a discrete metric that is related to the background
metric. 相似文献
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U. Einmahl 《Journal of Mathematical Sciences》2009,163(4):311-327
We provide a strong invariance principle for sums of independent, identically distributed random vectors that need not have
finite second absolute moments. Various applications are indicated. In particular, we show how one can re-obtain some recent
LIL type results from this invariance principle. Bibliography: 16 titles. 相似文献
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Our aim is to investigate a way to characterize the elements of a statistical manifold (the metric and the family of connections) using invariance properties suggested by Le Cam's theory of experiments. We distinguish the case where the statistical manifold is flat. Then, there naturally exists an entropy and it is proven that experiment invariance is equivalent to entropy invariance. If the statistical manifold is not flat, we introduce a notion of local invariance of selected order associated to the asymptotic (on n observations, n tending to infinity) expansion of the power of the Neymann Pearson test in a contiguous neighborough of some point. This invariance provides a substantial number of morphisms. This was not always true for the entropy invariance: particularly, the case of Gaussian experiments is investigated where it can be proven that entropy invariance does not characterize a metric or a family of connections. 相似文献
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Hong Jiaxing 《数学年刊B辑(英文版)》1986,7(2):160-173
This paper introduces the notion of the singular direction of wave front sets fordistributions and proves the invariance of the singular direction under the ellipticequivalent transformation.A kind of Fourier integral operators,which ensure suchinvariance,are also investigated.The results obtained are applied to the propagation ofsingularities for a class of differential operators with multiple characteristics. 相似文献
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Recently, Gowda and Sznajder [Gowda, M.S., Sznajder, R.: Automorphism invariance of P- and GUS-properties of linear transformations on Euclidean Jordan algebras. Math. Oper. Res. 31, 109–123 (2006)] have introduced and studied automorphism invariance of some P-properties for linear transformations. This paper deals with this automorphism invariance of some other complementarity properties, such as \(\hbox {E}_0,\,\hbox {P}_0\) , S, Z-properties. Particularly, we answer Gowda and Sznajder in positive that order P-property is algebra automorphism invariant in simple Jordan algebras. By replacing transposition with the invertibility in the concept of automorphism invariance, we propose a notion of similarity automorphism invariance. Most complementarity properties of linear transformations are also shown to be similarity invariant under algebra automorphisms and cone automorphisms. 相似文献
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N. A. Shananin 《Mathematical Notes》2010,88(5-6):879-887
Known results about the unique continuation of solutions of anisotropic linear and weakly nonlinear differential equations and the extension of the invariance property of these solutions are applied to prove theorems about the fiberwise quasianalyticity and the fiber structure of sets of symmetry invariance of solutions to quasilinear equations. 相似文献
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The problem of finding the nearest parametric approximation of a fuzzy number with respect to the average Euclidean distance is completely solved. Properties of translation invariance, scale invariance, additivity, preservation of expected value, value and ambiguity of this new approximation operator are studied and an algorithm for computing it is provided. 相似文献