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1.
We consider n nonintersecting Brownian motion paths with p prescribed starting positions at time t=0 and q prescribed ending positions at time t=1. The positions of the paths at any intermediate time are a determinantal point process, which in the case p=1 is equivalent to the eigenvalue distribution of a random matrix from the Gaussian unitary ensemble with external source.
For general p and q, we show that if a temperature parameter is sufficiently small, then the distribution of the Brownian paths is characterized
in the large n limit by a vector equilibrium problem with an interaction matrix that is based on a bipartite planar graph. Our proof is
based on a steepest descent analysis of an associated (p+q)×(p+q) matrix-valued Riemann–Hilbert problem whose solution is built out of multiple orthogonal polynomials. A new feature of the
steepest descent analysis is a systematic opening of a large number of global lenses. 相似文献
2.
The hypergeometric function type I distribution with the pdf proportional to x
ν−1(1−x)
γ−1
2
F
1(α,β;γ;1−x), 0<x<1 occurs as the distribution of the product of two independent beta variables. In this article, a multivariate generalization
of this distribution is defined and its properties are derived.
相似文献
3.
Let ℒ be an n-dimensional lattice, and let x be a point chosen uniformly from a large ball in ℝ
n
. In this note we consider the distribution of the distance from x to ℒ, normalized by the largest possible such distance (i.e., the covering radius of ℒ). By definition, the support of this
distribution is [0,1]. We show that there exists a universal constant α
2 that provides a natural “threshold” for this distribution in the following sense. For any ε>0, there exists a δ>0 such that for any lattice, this distribution has mass at least δ on [α
2−ε,1]; moreover, there exist lattices for which the distribution is tightly concentrated around α
2 (and so the mass on [α
2+ε,1] can be arbitrarily small). We also provide several bounds on α
2 and its extension to other ℓ
p
norms. We end with an application from the area of computational complexity. Namely, we show that α
2 is exactly the approximation factor of a certain natural
protocol for the Covering Radius Problem.
I. Haviv’s research was supported by the Binational Science Foundation and by the Israel Science Foundation.
V. Lyubashevsky’s research was supported by NSF ITR 0313241.
O. Regev’s research was supported by an Alon Fellowship, by the Binational Science Foundation, by the Israel Science Foundation,
and by the European Commission under the Integrated Project QAP funded by the IST directorate as Contract Number 015848. 相似文献
4.
Theodore Tachim Medjo 《Applied Mathematics and Optimization》2010,62(1):1-26
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian.
Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined
optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian
framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving
reflected BSDEs and the Snell envelope. 相似文献
5.
In this paper, we essentially compute the set of x,y>0 such that the mapping \(z\longmapsto(1-r+re^{z})^{x}(\frac{\lambda}{\lambda-z})^{y}\) is a Laplace transform. If X and Y are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by μ the distribution of X+Y. The above problem is equivalent to finding the set of x>0 such that μ *x exists. 相似文献
6.
Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems
Vicente Costanza Pablo S. Rivadeneira Ruben D. Spies 《Journal of Optimization Theory and Applications》2011,149(1):26-46
Partial differential equations for the unknown final state and initial costate arising in the Hamiltonian formulation of regular
optimal control problems with a quadratic final penalty are found. It is shown that the missing boundary conditions for Hamilton’s
canonical ordinary differential equations satisfy a system of first-order quasilinear vector partial differential equations
(PDEs), when the functional dependence of the H-optimal control in phase-space variables is explicitly known. Their solutions are computed in the context of nonlinear systems
with ℝ
n
-valued states. No special restrictions are imposed on the form of the Lagrangian cost term. Having calculated the initial
values of the costates, the optimal control can then be constructed from on-line integration of the corresponding 2n-dimensional Hamilton ordinary differential equations (ODEs). The off-line procedure requires finding two auxiliary n×n matrices that generalize those appearing in the solution of the differential Riccati equation (DRE) associated with the linear-quadratic
regulator (LQR) problem. In all equations, the independent variables are the finite time-horizon duration T and the final-penalty matrix coefficient S, so their solutions give information on a whole two-parameter family of control problems, which can be used for design purposes.
The mathematical treatment takes advantage from the symplectic structure of the Hamiltonian formalism, which allows one to
reformulate Bellman’s conjectures concerning the “invariant-embedding” methodology for two-point boundary-value problems.
Results for LQR problems are tested against solutions of the associated differential Riccati equation, and the attributes
of the two approaches are illustrated and discussed. Also, nonlinear problems are numerically solved and compared against
those obtained by using shooting techniques. 相似文献
7.
It is well-known that on a versal deformation of the Takens–Bogdanov bifurcation is possible to find dynamical systems that
undergo saddle-node, Hopf, and homoclinic bifurcations. In this document a nonlinear control system in the plane is considered,
whose nominal vector field has a double-zero eigenvalue, and then the idea is to find under which conditions there exists
a scalar control law such that be possible establish a priori, that the closed-loop system undergoes any of the three bifurcations: saddle-node, Hopf or homoclinic. We will say then that
such system undergoes the controllable Takens–Bogdanov bifurcation. Applications of this result to the averaged forced van der Pol oscillator, a population dynamics, and adaptive control systems
are discussed. 相似文献
8.
Consider an arbitrary transient random walk on ℤ
d
with d∈ℕ. Pick α∈[0,∞), and let L
n
(α) be the spatial sum of the αth power of the n-step local times of the walk. Hence, L
n
(0) is the range, L
n
(1)=n+1, and for integers α, L
n
(α) is the number of the α-fold self-intersections of the walk. We prove a strong law of large numbers for L
n
(α) as n→∞. Furthermore, we identify the asymptotic law of the local time in a random site uniformly distributed over the range. These
results complement and contrast analogous results for recurrent walks in two dimensions recently derived by Černy (Stoch.
Proc. Appl. 117:262–270, 2007). Although these assertions are certainly known to experts, we could find no proof in the literature in this generality.
相似文献
9.
Considering the Markov-binomial distribution, we obtain the moderate deviation and large deviation estimates for the number of successes S n and the number of experiments Y(r) until the rth success. 相似文献
10.
T. Tachim Medjo 《Applied Mathematics and Optimization》2011,63(1):75-106
We investigate in this article the Pontryagin’s maximum principle for control problem associated with the primitive equations (PEs) of the ocean with periodic inputs. We also derive a second-order sufficient condition for optimality. This work is closely related to Wang (SIAM J. Control Optim. 41(2):583–606, 2002) and He (Acta Math. Sci. Ser. B Engl. Ed. 26(4):729–734, 2006), in which the authors proved similar results for the three-dimensional Navier-Stokes (NS) systems. 相似文献
11.
In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control
set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems
can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as
unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions. 相似文献
12.
With a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables
defined by the orders of a function on irreducible components of the curve. The Poincaré series of this filtration turns out
to coincide with the Alexander polynomial of the curve germ. For a finite set of divisorial valuations on the ring corresponding
to some components of the exceptional divisor of a modification of the plane, in a previous paper there was obtained a formula
for the Poincaré series of the corresponding multi-index filtration similar to the one associated with plane germs. Here we
show that the Poincaré series of a set of divisorial valuations on the ring of germs of functions of two variables defines
“the topology of the set of the divisors” in the sense that it defines the minimal resolution of this set up to combinatorial
equivalence. For the plane curve singularity case, we also give a somewhat simpler proof of the statement by Yamamoto which
shows that the Alexander polynomial is equivalent to the embedded topology. 相似文献
13.
Pointwise estimates of the deviation T
n,A,B
f(⋅)−f(⋅) in terms of moduli of continuity [`(w)]·f\bar{w}_{\cdot}f and w
⋅
f are proved. Analog results on norm approximation with remarks and corollaries are also given. In the results essentially
weaker conditions than those in [2, Theorem 1, p. 437] are used. 相似文献
14.
The wealth of information that is available on the lattice of varieties of bands, is used to illuminate the structure of the lattice of sub-pseudovarieties of DA, a natural generalization of bands which plays an important role in language theory and in logic. The main result describes a hierarchy of decidable sub-pseudovarieties of DA in terms of iterated Mal’cev products with the pseudovarieties of definite and reverse definite semigroups. 相似文献
15.
Jiaqin Wei Hailiang Yang Rongming Wang 《Journal of Optimization Theory and Applications》2010,147(2):358-377
We consider the optimal proportional reinsurance and dividend strategy. The surplus process is modeled by the classical compound
Poisson risk model with regime switching. Considering a class of utility functions, the object of the insurer is to select
the reinsurance and dividend strategy that maximizes the expected total discounted utility of the shareholders until ruin.
By adapting the techniques and methods of stochastic control, we study the quasi-variational inequality for this classical
and impulse control problem and establish a verification theorem. We show that the optimal value function is characterized
as the unique viscosity solution of the corresponding quasi-variational inequality. 相似文献
16.
AbdulRahman Al-Hussein 《Applied Mathematics and Optimization》2011,63(3):385-400
We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation
is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator. 相似文献
17.
A. J. Zaslavski 《Journal of Optimization Theory and Applications》2010,145(3):597-612
We study the structure of solutions of a discrete-time control system with a compact metric space of states X which arises in economic dynamics. This control system is described by a nonempty closed set Ω⊂X×X which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous objective function v:Ω→R
1 which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are
independent of the length of the interval, for all sufficiently large intervals. In the present paper, we show that these
turnpike properties are stable under perturbations of the objective function v. 相似文献
18.
On the Distribution of Weakly Composite Numbers 总被引:1,自引:0,他引:1
OntheDistributionofWeaklyCompositeNumbers王天泽,李国强OntheDistributionofWeaklyCompositeNumbers¥WangTianze;LiGuoqiang(DepartmentofM... 相似文献
19.
In this paper, we explore the problem of isochronicity at infinity for a class of polynomial differential system. The technique is based on taking infinity into the origin by means of a homeomorphism. Simultaneously, we derive a recursive algorithm to compute period constants at the origin of the transformed system. At the end, as an application of our algorithm, we study pseudo-isochronous center conditions at infinity for a class of septic system. 相似文献
20.
M. Majewski 《Journal of Optimization Theory and Applications》2009,141(1):127-146
In this paper, we derive some results concerning the continuous dependence on parameters of optimal solutions to an optimal
control problem that involves a quasilinear hyperbolic differential equation with a boundary condition and a nonlinear integral
functional of action; continuous dependence of such kind is sometimes referred to as stability or sensitivity. To present
a sufficient condition for the continuous dependence, we use the Kuratowski–Painlevé upper limit of a sequence of sets. Also
offered is a technical interpretation of the results. 相似文献