首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 135 毫秒
1.
Let ξ12,... be independent random variables with distributions F1F2,... in a triangular array scheme (F i may depend on some parameter). Assume that Eξ i = 0, Eξ i 2 < ∞, and put \(S_n = \sum {_{i = 1}^n \;} \xi _i ,\;\overline S _n = \max _{k \leqslant n} S_k\). Assuming further that some regularly varying functions majorize or minorize the “averaged” distribution \(F = \frac{1}{n}\sum {_{i = 1}^n F_i }\), we find upper and lower bounds for the probabilities P(S n > x) and \(P(\bar S_n > x)\). We also study the asymptotics of these probabilities and of the probabilities that a trajectory {S k } crosses the remote boundary {g(k)}; that is, the asymptotics of P(maxkn(S k ? g(k)) > 0). The case n = ∞ is not excluded. We also estimate the distribution of the first crossing time.  相似文献   

2.
We obtain an integro-local limit theorem for the sum S(n) = ξ(1)+?+ξ(n) of independent identically distributed random variables with distribution whose right tail varies regularly; i.e., it has the form P(ξt) = t L(t) with β > 2 and some slowly varying function L(t). The theorem describes the asymptotic behavior on the whole positive half-axis of the probabilities P(S(n) ∈ [x, x + Δ)) as x → ∞ for a fixed Δ > 0; i.e., in the domain where the normal approximation applies, in the domain where S(n) is approximated by the distribution of its maximum term, as well as at the “junction” of these two domains.  相似文献   

3.
LetM be a connected two-dimensional Stein manifold withH 2(M,Z)=0 andSM a discrete subset withS≠ Ø. SetX:=M/S. Fix an integerr≥2. Then there exists a rankr vector bundleE onX such that there is no line bundleL onX with a non-zero mapLE.  相似文献   

4.
Hamiltonian cycles in Dirac graphs   总被引:1,自引:1,他引:0  
We prove that for any n-vertex Dirac graph (graph with minimum degree at least n/2) G=(V,E), the number, Ψ(G), of Hamiltonian cycles in G is at least
$exp_2 [2h(G) - n\log e - o(n)],$
where h(G)=maxΣ e x e log(1/x e ), the maximum over x: E → ?+ satisfying Σ e?υ x e = 1 for each υV, and log =log2. (A second paper will show that this bound is tight up to the o(n).)
We also show that for any (Dirac) G of minimum degree at least d, h(G) ≥ (n/2) logd, so that Ψ(G) > (d/(e + o(1))) n . In particular, this says that for any Dirac G we have Ψ(G) > n!/(2 + o(1)) n , confirming a conjecture of G. Sárközy, Selkow, and Szemerédi which was the original motivation for this work.  相似文献   

5.
Let X be a symmetric Banach function space on [0, 1] and let E be a symmetric (quasi)-Banach sequence space. Let f = {f k } k=1 n , n ≥ 1 be an arbitrary sequence of independent random variables in X and let {e k } k=1 ? E be the standard unit vector sequence in E. This paper presents a deterministic characterization of the quantity
$||||\sum\limits_{k = 1}^n {{f_k}{e_k}|{|_E}|{|_X}} $
in terms of the sum of disjoint copies of individual terms of f. We acknowledge key contributions by previous authors in detail in the introduction, however our approach is based on the important recent advances in the study of the Kruglov property of symmetric spaces made earlier by the authors. Authors acknowledge support from the ARC.
  相似文献   

6.
Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ?Q, then p=∞. Denote by DGL n np , n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL n np . In this work we intend to answer the following two questions: Given an object (L(V), ?) in DGL n 3n+2 and denote by S(L(V), ?) the class of objects homotopy equivalent to (L(V), ?). How we can characterize a free dgl to belong to S(L(V), ?)? Fix an object (L(V), ?) in DGL n 3n+2 . How many homotopy equivalence classes of objects (L(W), δ) in DGL n 3n+2 such that H * (W, d′)?H * (V, d) are there? Note that DGL n 3n+2 is a subcategory of DGL n np when p>3. Our tool to address this problem is the exact sequence of Whitehead associated with a free dgl.  相似文献   

7.
An IP system is a functionn taking finite subsets ofN to a commutative, additive group Ω satisfyingn(α∪β)=n(α)+n(β) whenever α∩β=ø. In an extension of their Szemerédi theorem for finitely many commuting measure preserving transformations, Furstenberg and Katznelson showed that ifS i ,1≤i≤k, are IP systems into a commutative (possibly infinitely generated) group Ω of measure preserving transformations of a probability space (X, B, μ, andAB with μ(A)>0, then for some ø≠α one has μ(? i=1 k S i({α})A>0). We extend this to so-called FVIP systems, which are polynomial analogs of IP systems, thereby generalizing as well joint work by the author and V. Bergelson concerning special FVIP systems of the formS(α)=T(p(n(α))), wherep:Z t Z d is a polynomial vanishing at zero,T is a measure preservingZ d action andn is an IP system intoZ t . The primary novelty here is potential infinite generation of the underlying group action, however there are new applications inZ d as well, for example multiple recurrence along a wide class ofgeneralized polynomials (very roughly, functions built out of regular polynomials by iterated use of the greatest integer function).  相似文献   

8.
This paper is devoted to the compactness of the hypercomplex commutator S γ M a ? M a S γ, where S γ is the Cauchy singular integral operator (in the Douglis sense), a is a Hölder continuous hypercomplex function and M a is the multiplication operator given by M a f = a f. We extend a known compactness sufficient condition for the commutator of the Cauchy singular integral operator to the frame of the hypercomplex analysis, where γ is merely required to be an arbitrary regular closed Jordan curve.  相似文献   

9.
10.
We consider the problem of searching for a best LAD-solution of an overdetermined system of linear equations Xa=z, X∈?m×n, mn, \(\mathbf{a}\in \mathbb{R}^{n}, \mathbf {z}\in\mathbb{R}^{m}\). This problem is equivalent to the problem of determining a best LAD-hyperplane x?a T x, x∈? n on the basis of given data \((\mathbf{x}_{i},z_{i}), \mathbf{x}_{i}= (x_{1}^{(i)},\ldots,x_{n}^{(i)})^{T}\in \mathbb{R}^{n}, z_{i}\in\mathbb{R}, i=1,\ldots,m\), whereby the minimizing functional is of the form
$F(\mathbf{a})=\|\mathbf{z}-\mathbf{Xa}\|_1=\sum_{i=1}^m|z_i-\mathbf {a}^T\mathbf{x}_i|.$
An iterative procedure is constructed as a sequence of weighted median problems, which gives the solution in finitely many steps. A criterion of optimality follows from the fact that the minimizing functional F is convex, and therefore the point a ?∈? n is the point of a global minimum of the functional F if and only if 0?F(a ?).
Motivation for the construction of the algorithm was found in a geometrically visible algorithm for determining a best LAD-plane (x,y)?αx+βy, passing through the origin of the coordinate system, on the basis of the data (x i ,y i ,z i ),i=1,…,m.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号