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1.
Jerzy Szulga 《Probability Theory and Related Fields》1992,94(1):83-90
Summary If (Y
i) and (V
i) are independent random sequences such thatY
i are i.i.d. random variables belonging to the normal domain of attraction of a symmetric -stable law, 0<<2, andV
i are i.i.d. random variables, then the limit distributions of U-statistics
, coincide with the probability laws of multiple stochastic integralsX
d
f = ...
f (t
1, ... ,t
d)dX(t
d) with respect to a symmetric -stable processX(t).The research was originated during author's visit at ORIE, Cornell University 相似文献
2.
Lin Zhengyan 《数学学报(英文版)》1989,5(2):185-192
Consider the weighted sums
of a sequence {X
n} of independent random variables or random elements inD [0,1]. For convergence ofS
n in probability and with probability one, in [2],[3] etc., the following stronger condition is required: {X
n} is uniformly bounded by a random variableX,i.e.P(¦X
n¦x)P(¦X¦x) for allx>0. Our paper aims at trying to drop this restriction.The Project supported by National Natural Science Foundation of China 相似文献
3.
We present some comments on the behavior of solutions of the difference equation
where p
i 0, i = 1,..., k, k N, and x
–k
,..., x
–1 R. 相似文献
4.
We obtain precise large deviations for heavy-tailed random sums
, of independent random variables.
are nonnegative integer-valued random variables independent of r.v. (X
i
)i
N with distribution functions F
i. We assume that the average of right tails of distribution functions F
i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given. 相似文献
5.
Critical behavior of the Gaussian model on fractal lattices in external magnetic field 总被引:4,自引:0,他引:4
For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution
constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation
holds among bq's, where bq is the Gaussian type distribution constant of site j. Using the decimation real-space renormalization group following the
spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves
and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor
interaction and the magnetic field of site j can be expressed in the form
respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For
the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if
the fractal dimensionalityd
f=4, the Gaussian model and the mean field theories give the same results. 相似文献
6.
Vladislav Kargin 《Probability Theory and Related Fields》2007,139(3-4):397-413
Let X
i
denote free identically-distributed random variables. This paper investigates how the norm of products behaves as n approaches infinity. In addition, for positive X
i
it studies the asymptotic behavior of the norm of where denotes the symmetric product of two positive operators: . It is proved that if EX
i
= 1, then is between and c
2
n for certain constant c
1 and c
2. For it is proved that the limit of exists and equals Finally, if π is a cyclic representation of the algebra generated by X
i
, and if ξ is a cyclic vector, then for all n. These results are significantly different from analogous results for commuting random variables. 相似文献
7.
Complete convergence and almost sure convergence of weighted sums of random variables 总被引:6,自引:0,他引:6
Deli Li M. Bhaskara Rao Tiefeng Jiang Xiangchen Wang 《Journal of Theoretical Probability》1995,8(1):49-76
Letr>1. For eachn1, let {X
nk
, –<k<} be a sequence of independent real random variables. We provide some very relaxed conditions which will guarantee
for every >0. This result is used to establish some results on complete convergence for weighted sums of independent random variables. The main idea is that we devise an effetive way of combining a certain maximal inequality of Hoffmann-Jørgensen and rates of convergence in the Weak Law of Large Numbers to establish results on complete convergence of weighted sums of independent random variables. New results as well as simple new proofs of known ones illustrate the usefulness of our method in this context. We show further that this approach can be used in the study of almost sure convergence for weighted sums of independent random variables. Convergence rates in the almost sure convergence of some summability methods ofiid random variables are also established. 相似文献
8.
V. A. Baranova 《Mathematical Notes》1972,12(2):510-512
In the class S of functions
which are regular and single-sheeted in the circle ¦z¦ < 1, the bound for ¦c4¦ in terms of ¦c2¦, obtained by Al'fors, is improved. The crudest bound ¦c4¦ –< 4/15 (11 + ¦c2¦) is better than that of Al'fors: ¦c4¦ –<
Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 127–130, August, 1972. 相似文献
9.
J. Sunklodas 《Lithuanian Mathematical Journal》2001,41(3):292-305
We derive lower bounds for Lp norms
, in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments. 相似文献
10.
Jürg Hüsler 《Probability Theory and Related Fields》1983,63(2):257-270
Summary Let {X
i
, i1} be a random sequence and {u
ni
,1in, n1} be an array of boundary values. We consider the asymptotic approximation of the probability P
n
=P{X
i
u
ni
,1in} by
. We give sufficient conditions on X
i such that P
n–P
n
*
0 as n. This generalizes the situation considered in extreme-value theory where the boundary is constant in i. The general theory is applied in particular to Gaussian cases. 相似文献
11.
M. L. Gromov 《Mathematical Notes》1968,3(5):326-332
Combinatorial invariants of a finite simplicial complex K are considered that are functions of the number i(K) of Simplexes of dimension i of this complex. The main result is Theorem 2, which gives the necessary and sufficient condition for two complexes K and L to have subdivisions K' and L' such that i(K')=i(L') for 0 . The theorem yields a corollary: if the polyhedra ¦K¦ and ¦L¦ are homeomorphic, then there exist subdivisions K' and L' such that i(K')=i(L') for i0.Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 511–522, May, 1968. 相似文献
12.
Let r
1, …, r
s
be non-zero integers satisfying r
1 + ⋯ + r
s
= 0. Let G be a finite abelian group with k
i
|k
i-1(2 ≤ i ≤ n), and suppose that (r
i
, k
1) = 1(1 ≤ i ≤ s). Let denote the maximal cardinality of a set which contains no non-trivial solution of r
1
x
1 + ⋯ + r
s
x
s
= 0 with . We prove that . We also apply this result to study problems in finite projective spaces.
相似文献
13.
Thomas M. Lewis 《Journal of Theoretical Probability》2001,14(2):357-378
In this paper, we construct stationary sequences of random variables {
i
: i0} taking values ±1 with probability 1/2 and we prove an Erdös–Rényi law of large numbers for the length of the longest run of consecutive +1's in the sample {0,...,
n
}. Our model, which is called random walk in random scenery, exhibits long-range, positive dependence. 相似文献
14.
It is proposed that the Gaussian type distribution constantb
qi in the Gaussian model depends on the coordination numberq
i of sitei, and that the relation
holds amongb
qi
’s. The Gaussian model is then studied on a family of the diamond-type hierarchical (or DH) lattices, by the decimation real-space
renormalization group following spin-rescaling method. It is found that the magnetic property of the Gaussian model belongs
to the same universal class, and that the critical pointK* and the critical exponentv are given by
and
, respectively.
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research 相似文献
15.
Let Xi, i = 1, 2,…, be i.i.d. symmetric random variables in the domain of attraction of a symmetric stable distribution Gα with 0 < α < 2. Let Yi, i = 1, 2, …, be i.i.d. symmetric stable random variables with the common distribution Gα. It is known that under certain conditions the sequences {Xi} and {Yi} can be reconstructed on a new probability space without changing the distribution of each such that \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{i = 1}^n {(X_i - Y_i) = o(n^{1/\gamma})} $\end{document} a.s. as n → ∞, where α ≦ γ < 2 (see Stout [10]). We will give a second approximation by partial sums of i.i.d. stable (with characteristic exponent α*, α < α* ≦ 2) random variables Ui, i = 1, 2,…, n, and we will obtain strong upperbounds for the differences \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{i = 1}^n {(X_i - Y_i - U_i)} $\end{document}. 相似文献
16.
Summary Consider the regression model Y
i
*
=g(x
i
*
)+e
i
*
, i=1,2,...,n, where x
i
*
's denote unordered design variables, and g is an unknown function defined on the interval [0,1]. Assume {e
i
*
} are iid random variables with zero mean and finite variance. Priestley and Chao (1972) and Clark (1977) proposed estimators g
2n
and g
3n
, respectively for g. In this paper, the asymptotic behavior of g
2n
and g
3n
is studied utilizing the properties of the new estimator g
1n
. It is shown that g
1n
, g
2n
, g
3n
are asymptotically equivalent in various senses. Moreover, consistency results are established and rates of uniform convergence obtained. For example, if E¦e
*¦3<, if g is Lipschitz of order 1, and if {n} is any sequence of constants tending to as n, then for all
, as n. Finally, when g is monotone, a strong consistent isotonic estimator g
n
*
is considered. 相似文献
17.
Summary A one-dimensional chain of nearest neighbor linearly interacting oscillators {q
x
}
x
is studied. The set of all its extremal DLR measures is characterized in terms of a parameter 2. For each there is a Gaussian DLR measure with support on the set of configurations determined by the rate of growth of¦q
x¦. It is then finally proved that there is only one translationally invariant DLR measure. This proves the following conjecture: invariant DLR measures give uniformly finite first moment to ¦q
x¦. 相似文献
18.
Complete moment and integral convergence for sums of negatively associated random variables 总被引:2,自引:0,他引:2
For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE(max1≤k≤n|Sk|^1/q-∈bn^1/qp)^+〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 (log n) ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence. 相似文献
19.
M. N. Sheremeta 《Mathematical Notes》1975,18(3):823-827
Suppose thatf(z) is an entire transcendental function with real Taylor coefficients, M(r)= max¦f(z)¦on¦z¦=r, and {n} is the sequence of sign changes of the coefficients. We will show that if (1/n)<, then
.Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 395–402, September, 1975.The author thanks A. A. Gol'dberg for his useful comments. 相似文献
20.
F. Morits 《Mathematical Notes》1975,17(2):127-133
Let {Xi}
–
be a sequence of random variables, E(Xi) 0. If 1, estimates for the -th moments
can be derived from known estimates
of the -th moment. Here we generalized the Men'shov-Rademacher inequality for =2 for orthonormal Xi, to the case 1 and dependent random variables. The Men'shov-Payley inequality >2 for orthonormal Xi) is generalized for >2 to general random variables. A theorem is also proved that contains both the Erdös -Stechkin theorem and Serfling's theorem withv > 2 for dependent random variables.Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 219–230, February, 1975.This article was written while the author was working in the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR. 相似文献