共查询到20条相似文献,搜索用时 31 毫秒
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In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on and by a vector-valued measure on , respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton–Jacobi–Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game. 相似文献
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Ekaterina Vl. Bulinskaya 《Stochastic Processes and their Applications》2018,128(7):2325-2340
For a supercritical catalytic branching random walk on , , with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation. 相似文献
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《Indagationes Mathematicae》2014,25(5):846-871
We introduce the notion of tropicalization for Poisson structures on with coefficients in Laurent polynomials. To such a Poisson structure we associate a polyhedral cone and a constant Poisson bracket on this cone. There is a version of this formalism applicable to viewed as a real Poisson manifold. In this case, the tropicalization gives rise to a completely integrable system with action variables taking values in a polyhedral cone and angle variables spanning a torus.As an example, we consider the canonical Poisson bracket on the dual Poisson–Lie group for in the cluster coordinates of Fomin–Zelevinsky defined by a certain choice of solid minors. We prove that the corresponding integrable system is isomorphic to the Gelfand–Zeitlin completely integrable system of Guillemin–Sternberg and Flaschka–Ratiu. 相似文献
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Xianwen Zhang 《Applied Mathematics Letters》2013,26(11):1087-1093
We prove the existence of a global nonnegative weak solution to the Cauchy problem of the Vlasov–Poisson–BGK system for initial datum having finite mass and energy and belonging to with . 相似文献
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Let denote the unit sphere in the Euclidean space . We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on . We obtain both upper bound and lower bound estimates. We then use these inequalities to estimate the discrepancy of the normalized counting measures associated with minimal energy configurations on . 相似文献
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We consider the nonlinear Schrödinger equations (NLS) on with random and rough initial data. By working in the framework of spaces, , we prove almost sure local well-posedness for rougher initial data than those considered in the existing literature. The main ingredient of the proof is the dispersive estimate. 相似文献
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Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
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A second order asymptotic expansion in the local limit theorem for a simple branching random walk in
Zhi-Qiang Gao 《Stochastic Processes and their Applications》2018,128(12):4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on , which is used in the proof of the main theorem and is of independent interest. 相似文献
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This paper uses a connection between bounded remainder sets in
and cut-and-project sets in together with the fact that each one-dimensional Pisot substitution sequence is bounded distance equivalent to some lattice in order to construct several bounded remainder sets with fractal boundary. Moreover it is shown that there are cut-and-project sets being not bounded distance equivalent to each other even if they are locally indistinguishable, more precisely: even if they are contained in the same hull. 相似文献
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We prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators. Namely, we show holomorphic extension to a sector in the complex domain, with a corresponding Gaussian decay, according to the basic properties of the Hermite functions in . Our results apply, in particular, to nonlinear eigenvalue problems for the harmonic oscillator associated to a real-analytic scattering, or asymptotically conic, metric in , as well as to certain perturbations of the classical harmonic oscillator. 相似文献
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