共查询到20条相似文献,搜索用时 31 毫秒
1.
Kimberly K. J. Kinateder Patrick McDonald 《Proceedings of the American Mathematical Society》1997,125(6):1815-1822
Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
2.
Takeyuki Hida 《Acta Appl Math》1994,35(1-2):49-61
We discuss stochastic variational calculus for a random field {X(C)},C being a surface in a Euclidean space, which lives in the space of generalized white noise functionals. The infinite-dimensional rotation group plays important roles in the calculus. 相似文献
3.
Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular,
dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent
functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic
Wiener functionals, including Lévy’s stochastic area and the square norm of Brownian paths. In the infinite variance case,
various tail estimates such as stable ones are also presented.
相似文献
4.
Jean-Sébastien Le Brizaut 《Bulletin des Sciences Mathématiques》2002,126(8):693-703
Minima of nonconvex functionals acting on the Euclidean space are determined by stochastic methods. Feasible conditions for the algotihms are stated. 相似文献
5.
关于高维Willmore问题 总被引:3,自引:0,他引:3
本文考虑高维欧氏空间中子流形M的一组有较好意义的共形不变的泛函.给出这些泛函通过M的Betti数的下界估计;给出对于管状超曲面的下界和对于双球环的下界以及达到这些下界的相应的子流形,并且证明对于管状超曲面所得的有关Betti数的下界是不精确的,方法是不适当的.给出类似Willmore猜测的一些猜测. 相似文献
6.
Mathematical Notes - We consider sums of exponentially stabilizing functionals (introduced by Penrose and Yukich) of Poisson point processes in d-dimensional Euclidean space. The asymptotic... 相似文献
7.
S. B. Makarova 《Journal of Mathematical Sciences》1988,43(6):2818-2822
An estimate is given of the mean value with respect to a Gaussian measure of the distance between distributions of two finite collections of linear functionals over a Euclidean space with probability measure for certain metrics in the space of finite-dimensional distributions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 115–121, 1987. 相似文献
8.
Horst Osswald 《Journal of Theoretical Probability》2009,22(2):441-473
An approach to Malliavin calculus for Lévy processes, discrete in time and smooth in chance, is presented. Each Lévy triple
can be satisfied by a Lévy process living on a fixed sample space Ω, which is, in a certain sense, a finite dimensional Euclidean
space. The probability measures on Ω characterize the Lévy processes. We compare these measures with the associated Lévy measures,
and present several examples. Using chaos expansions for Lévy functionals, even for those having no moments, we can represent
all these functionals by polynomials in several variables. There exists an effective method to compute the kernels of the
chaos decomposition. Finally, we point out several applications, which are postponed to a succession of papers.
Dedicated to Helmut Schwichtenberg. 相似文献
9.
K. K. J. Kinateder Patrick McDonald David Miller 《Probability Theory and Related Fields》1998,111(4):469-487
Let X
t
be a diffusion in Euclidean space. We initiate a study of the geometry of smoothly bounded domains in Euclidean space using
the moments of the exit time for particles driven by X
t
, as functionals on the space of smoothly bounded domains. We provide a characterization of critical points for each functional
in terms of an overdetermined boundary value problem. For Brownian motion we prove that, for each functional, the boundary
value problem which characterizes critical points admits solutions if and only if the critical point is a ball, and that all
critical points are maxima.
Received: 23 January 1997 / Revised version: 21 January 1998 相似文献
10.
Menita Carozza Hongya Gao Raffaella Giova Francesco Leonetti 《Journal of Optimization Theory and Applications》2018,178(3):699-725
We consider polyconvex functionals of the Calculus of Variations defined on maps from the three-dimensional Euclidean space into itself. Counterexamples show that minimizers need not to be bounded. We find conditions on the structure of the functional, which force minimizers to be locally bounded. 相似文献
11.
Roger Moser 《Mathematische Zeitschrift》2013,273(3-4):771-792
For surfaces embedded in a three-dimensional Euclidean space, consider a functional consisting of two terms: a version of the Willmore energy and an anisotropic area penalising the first component of the normal vector, the latter weighted with the factor ${1/\epsilon^2}$ . The asymptotic behaviour of such functionals as ${\epsilon}$ tends to 0 is studied in this paper. The results include a lower and an upper bound on the minimal energy subject to suitable constraints. Moreover, for embedded spheres, a compactness result is obtained under appropriate energy bounds. 相似文献
12.
This paper is concerned with the relations between the differential invariants of a smooth manifold embedded in the Euclidean
space and the square of the distance function from the manifold. In particular, we are interested in curvature invariants
like the mean curvature vector and the second fundamental form. We find that these invariants can be computed in a very simple
way using the third order derivatives of the squared distance function. Moreover, we study a general class of functionals
depending on the derivatives up to a given order γ of the squared distance function and we find an algorithm for the computation
of the Euler equation. Our class of functionals includes as particular cases the well-known area functional (γ = 2), the integral
of the square of the quadratic norm of the second fundamental form (γ = 3), and the Willmore functional. 相似文献
13.
We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem. 相似文献
14.
We extend to a functional setting the concept of quermassintegrals, well-known within the Minkowski theory of convex bodies. We work in the class of quasi-concave functions defined on the Euclidean space, and with the hierarchy of their subclasses given by α-concave functions. In this setting, we investigate the most relevant features of functional quermassintegrals, and we show they inherit the basic properties of their classical geometric counterpart. As a first main result, we prove a Steiner-type formula which holds true by choosing a suitable functional equivalent of the unit ball. Then we establish concavity inequalities for quermassintegrals and for other general hyperbolic functionals, which generalize the celebrated Prékopa–Leindler and Brascamp–Lieb inequalities. Further issues that we transpose to this functional setting are integral-geometric formulae of Cauchy–Kubota type, valuation property and isoperimetric/Urysohn-like inequalities. 相似文献
15.
《Optimization》2012,61(4-5):441-458
We consider the Hamiltonian cycle problem (HCP) embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of long-run state-action frequencies induced by the MDP's stationary policies. We also consider two quadratic functionals over the same space. We show that when the perturbation parameter, ? is sufficiently small the Hamiltonian cycles of the given directed graph are precisely the maximizers of one of these quadratic functionals over the frequency space intersected with an appropriate (single) contour of the second quadratic functional. In particular, all these maximizers have a known Euclidean distance of z m (?) from the origin. Geometrically, this means that Hamiltonian cycles, if any, are the points in the frequency polytope where the circle of radius z m (?) intersects a certain ellipsoid. 相似文献
16.
Consider a homogeneous Poisson point process in a compact convex set in d‐dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point process with its nearest neighbour that is closer to the origin. For increasing intensity of the underlying Poisson point process the paper provides expectation and variance asymptotics as well as central limit theorems with rates of convergence for a class of edge functionals including the total edge length. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 262–286, 2017 相似文献
17.
We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients. 相似文献
18.
19.
New results related to the decomposition theorem of additive functionals associated to quasi-regular Dirichlet forms are presented. A characterization of subordinate processes associated to quasi-regular symmetric Dirichlet forms in terms of the unique solutions of the corresponding martingale problems is obtained.The subordinate of (generalized) Ornstein-Uhlenbeck processes are exhibited explicitly in terms of generators, Dirichlet forms, and unique pathwise solutions of stochastic differential equations (SDEs). In the case where the state space is infinite dimensional as, e.g. in Euclidean quantum field theory, the construction provides a characterization of the processes in terms of projections on the topological dual space, and corresponding finite-dimensional SDEs. 相似文献
20.
We prove Brunn-Minkowski type inequalities for three new functionals which are power moments for conformal and Euclidean characteristics of domains. 相似文献