共查询到20条相似文献,搜索用时 171 毫秒
1.
James Allen Fill 《Journal of Theoretical Probability》2009,22(3):543-557
A well-known theorem usually attributed to Keilson states that, for an irreducible continuous-time birth-and-death chain on
the nonnegative integers and any d, the passage time from state 0 to state d is distributed as a sum of d independent exponential random variables. Until now, no probabilistic proof of the theorem has been known. In this paper
we use the theory of strong stationary duality to give a stochastic proof of a similar result for discrete-time birth-and-death
chains and geometric random variables, and the continuous-time result (which can also be given a direct stochastic proof)
then follows immediately. In both cases we link the parameters of the distributions to eigenvalue information about the chain.
We also discuss how the continuous-time result leads to a proof of the Ray–Knight theorem.
Intimately related to the passage-time theorem is a theorem of Fill that any fastest strong stationary time T for an ergodic birth-and-death chain on {0,…,d} in continuous time with generator G, started in state 0, is distributed as a sum of d independent exponential random variables whose rate parameters are the nonzero eigenvalues of −G. Our approach yields the first (sample-path) construction of such a T for which individual such exponentials summing to T can be explicitly identified.
Research of J.A. Fill was supported by NSF grant DMS–0406104 and by The Johns Hopkins University’s Acheson J. Duncan Fund
for the Advancement of Research in Statistics. 相似文献
2.
The classical Mason–Stothers theorem deals with nontrivial polynomial solutions to the equation a + b = c. It provides a lower bound on the number of distinct zeros of the polynomial abc in terms of deg a, deg b and deg c. We extend this to general analytic functions living on a reasonable bounded domain
W ì \mathbb C{\Omega\subset{\mathbb C}}, rather than on the whole of
\mathbb C{{\mathbb C}}. The estimates obtained are sharp, for any Ω, and a generalization of the original result on polynomials can be recovered
from them by a limiting argument. 相似文献
3.
The approximate sampling theorem with its associated aliasing error is due to J.L. Brown (1957). This theorem includes the classical Whittaker–Kotel’nikov–Shannon theorem as a special case. The converse is established in the present paper, that is, the classical sampling theorem for , 1p<∞, w>0, implies the approximate sampling theorem. Consequently, both sampling theorems are fully equivalent in the uniform norm.Turning now to -space, it is shown that the classical sampling theorem for , 1<p<∞ (here p=1 must be excluded), implies the -approximate sampling theorem with convergence in the -norm, provided that f is locally Riemann integrable and belongs to a certain class Λp. Basic in the proof is an intricate result on the representation of the integral as the limit of an infinite Riemann sum of |f|p for a general family of partitions of ; it is related to results of O. Shisha et al. (1973–1978) on simply integrable functions and functions of bounded coarse variation on . These theorems give the missing link between two groups of major equivalent theorems; this will lead to the solution of a conjecture raised a dozen years ago. 相似文献
4.
Vrećica 《Discrete and Computational Geometry》2003,29(4):505-510
Abstract. In 1989 Helge Tverberg proposed a quite general conjecture in Discrete Geometry, which could be considered as the common
basis for many results in Combinatorial Geometry, and at the same time as a discrete analogue of the common transversal theorems.
It implies or contains as special cases many classical ``coincidence' results such as Radon's theorem, Rado's theorem, the
Ham sandwich theorem, ``non-embeddability' results (e.g. non-embeddability of graphs K
5
and K
3,3
in R
2
), etc. The main goal of this short note is to verify this conjecture in one new, non-trivial case. We obtain the continuous
version of the conjecture. So, it is not surprising that we use topological methods, or more precisely the methods of equivariant
topology and the theory of characteristic classes. 相似文献
5.
We consider sufficient conditions for a degree sequence π to be forcibly k-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree
sequence to be potentially k-factor graphical. We first give a theorem for π to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most β ≥ 0. These theorems are equal in strength to Chvátal’s well-known hamiltonian theorem, i.e., the best monotone degree condition
for hamiltonicity. We then give an equally strong theorem for π to be forcibly 2-factor graphical. Unfortunately, the number of nonredundant conditions that must be checked increases significantly
in moving from k = 1 to k = 2, and we conjecture that the number of nonredundant conditions in a best monotone theorem for a k-factor will increase superpolynomially in k. This suggests the desirability of finding a theorem for π to be forcibly k-factor graphical whose algorithmic complexity grows more slowly. In the final section, we present such a theorem for any
k ≥ 2, based on Tutte’s well-known factor theorem. While this theorem is not best monotone, we show that it is nevertheless
tight in a precise way, and give examples illustrating this tightness. 相似文献
6.
We introduce a notion of derived Azumaya algebras over ring and schemes generalizing the notion of Azumaya algebras of Grothendieck (Le groupe de Brauer. I. Algèbres d’Azumaya et interprétations diverses. Dix Exposés sur la Cohomologie des Schémas, pp. 46–66, North-Holland, Amsterdam, 1968). We prove that any such algebra B on a scheme X provides a class ϕ(B) in . We prove that for X a quasi-compact and quasi-separated scheme ϕ defines a bijective correspondence, and in particular that any class in , torsion or not, can be represented by a derived Azumaya algebra on X. Our result is a consequence of a more general theorem about the existence of compact generators in twisted derived categories, with coefficients in any local system of reasonable dg-categories, generalizing the well known existence of compact generators in derived categories of quasi-coherent sheaves of Bondal and Van Den Bergh (Mosc. Math. J. 3(1):1–36, 2003). A huge part of this paper concerns the treatment of twisted derived categories, as well as the proof that the existence of compact generator locally for the fppf topology implies the existence of a global compact generator. We present explicit examples of derived Azumaya algebras that are not represented by classical Azumaya algebras, as well as applications of our main result to the localization for twisted algebraic K-theory and to the stability of saturated dg-categories by direct push-forwards along smooth and proper maps. 相似文献
7.
8.
Jürgen Pöschel 《Mathematische Annalen》2011,349(2):433-458
We describe a new, short proof of some facts relating the gap lengths of the spectrum of a potential q of Hill’s equation, −y′′ + qy = λy, to its regularity. For example, a real potential is in a weighted Gevrey-Sobolev space if and only if its gap lengths, γ
n
, belong to a similarly weighted sequence space. An extension of this result to complex potentials is proven as well. We also
recover Trubowitz results about analytic potentials. The proof essentially employs the implicit function theorem. 相似文献
9.
We establish a stochastic nonlinear analogue of the Perron–Frobenius theorem on eigenvalues and eigenvectors of positive matrices.
The result is formulated in terms of an automorphism T of a probability space and a random transformation D of the non-negative cone of an n-dimensional Euclidean space. Under assumptions of monotonicity and homogeneity of D, we prove the existence of scalar and vector measurable functions α > 0 and x > 0 satisfying the equation αTx = D(x) almost surely. We apply the result obtained to the analysis of a class of random dynamical systems arising in mathematical
economics and finance (von Neumann–Gale dynamical systems). 相似文献
10.
Klaus Metsch 《Designs, Codes and Cryptography》2011,60(3):277-282
The famous Dembowski-Wagner theorem gives various characterizations of the classical geometric 2-design PG
n-1(n, q) among all 2-designs with the same parameters. One of the characterizations requires that all lines have size q + 1. It was conjectured [2] that this is also true for the designs PG
d
(n, q) with 2 ≤ d ≤ n − 1. We establish this conjecture, hereby improving various previous results. 相似文献
11.
Matt Kerr 《K-Theory》2003,29(3):175-210
The classical Abel–Jacobi map is used to geometrically motivate the construction of regulator maps from Milnor K-groups K
n
M
(C(X)) to Deligne cohomology. These maps are given in terms of some new, explicit (n – 1)-currents, higher residues of which are defined and related to polylogarithms. We study their behavior in families X
s
and prove a rigidity result for the regulator image of the Tame kernel, which leads to a vanishing theorem for very general complete intersections. 相似文献
12.
13.
Abstract We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration and the classical Itô stochastic calculus. The existence result is based on the Yamada–Watanabe theorem. 相似文献
14.
We prove in this paper that the boundary spectral data, i.e. the Dirichlet eigenvalues and normal derivatives of the eigenfunctions at the boundary uniquely determines a potential in Lp on bounded domains. This result generalizes the result of Nachman, Sylvester and Uhlmann to unbounded potentials. This result can be viewed as a generalization of the classical one-dimensional Borg–Levinson theorem. 相似文献
15.
Let E be a CM elliptic curve defined over ℚ and of conductor N. We establish an asymptotic formula, uniform in N and with improved error term, for the counting function of primes p for which the reduction mod p of E is cyclic. Our result resembles the classical Siegel-Walfisz theorem regarding the distribution of primes in arithmetic progressions. 相似文献
16.
Grega Cigler Roman Drnovšek Damjana Kokol-Bukovšek Matja? Omladi? Thomas J. Laffey Heydar Radjavi Peter Rosenthal 《Journal of Functional Analysis》1998,160(2):245
T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable. 相似文献
17.
We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C1-boundary, the other stated for sets with finite perimeter. 相似文献
18.
Christopher Hollings 《Semigroup Forum》2010,80(3):453-476
We extend the ‘∨-premorphisms’ part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive
categories, following on from a result of Lawson (J. Algebra 141:422–462, 1991) for the ‘morphisms’ part. However, it is so-called ‘∧-premorphisms’ which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type
theorem for (ordered) ∧-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem
in the inverse case. 相似文献
19.
Pierre Dèbes 《manuscripta mathematica》1996,89(1):107-137
A classical tool for studying Hilbert's irreducibility theorem is Siegel's finiteness theorem forS-integral points on algebraic curves. We present a different approach based ons-integral points rather thanS-integral points. Given an integers>0, an elementt of a fieldK is said to bes-integral if the set of placesv ∈M
K for which |t|v > l is of cardinality ≤s (instead of contained inS for “S-integral”). We prove a general diophantine result fors-integral points (Th.1.4). This result, unlike Siegel's theorem, is effective and is valid more generally for fields with
the product formula. The main application to Hilbert's irreducibility theorem is a general criterion for a given Hilbert subset
to contain values of given rational functions (Th.2.1). This criterion gives rise to very concrete applications: several examples
are given (§2.5). Taking advantage of the effectiveness of our method, we can also produce elements of a given Hilbert subset
of a number field with explicitely bounded height (Cor.3.7). Other applications, including the case thatK is of characteristicp>0, will be given in forthcoming papers ([8], [9]). 相似文献
20.
Richard Resco 《Israel Journal of Mathematics》1979,32(2-3):236-256
In this paper we prove the following theorem:
Let D be a division ring with center the field k, and let k (x
1, …, xn) denote the rational function field in n variables over k. If D contains a maximal subfield which has transcendence degree
at least n over k, then D ⊗k k (x1, …, xn) is a simple Noetherian domain of Krull and global dimensions n.
Rather surprisingly, the preceding result can be used to determine the maximum transcendence degrees of the commutative subalgebras
of several classically studied division rings. Using the theorem we prove, for example, that in the division ring of quotients
of the Weyl algebra,A
n, every maximal subfield has transcendence degree at mostn over the center. 相似文献