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1.
D. J. Daley 《Probability Theory and Related Fields》1981,58(2):199-203
Summary The sum a
n
X
n
of a weighted series of a sequence {X
n
} of identically distributed (not necessarily independent) random variables (r.v.s.) is a.s. absolutely convergent if for some in 0<1, ¦a
n
¦ < and E¦X
n
¦ < ; if a
n
=z
n
for some ¦z¦<1 then it suffices that E(log¦X
n
¦)+<. Examples show that these sufficient conditions are not necessary. For mutually independent {X
n
} necessary conditions can be given: the a.s. absolute convergence of X
n
z
n
(all ¦z¦<1) then implies E(log¦X
n
¦)+ < , while if the X
n
are non-negative stable r.v.s. of index , ¦a
n
X
n
¦< if and only if ¦a
n
¦ < . 相似文献
2.
N. P. Korneichuk 《Mathematical Notes》1971,10(5):719-723
In the Lp(a, b) space the exact values of n-diameters (n=1, 2, ...) are found of the class H[a, b] of the functions f(x) such that ¦f(x)-f(x)¦ (¦x-x¦), where (t) is a given continuity module which is convex upwards.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 493–500, November, 1971. 相似文献
3.
E. Csáki 《Probability Theory and Related Fields》1980,54(3):287-301
Summary Let W(t) be a standard Wiener process and let f(x) be a function from the compact class in Strassen's law of the iterated logarithm. We investigate the lim inf behavior of the variable sup ¦W(xT)(2T loglog T)–1/2–f(x)¦, 0x1 suitably normalized as T.This extends Chung's result valid for f(x)0, stating that lim inf.[ sup ¦(2T loglogT)–1/2
W(xT)¦(loglog T)–1]=/4 a.s. T 0x1 相似文献
4.
We establish conditions under which the relation M(x, F) (x, F) m(x, F) holds except for a small set, as ¦x¦ + for an entire function F(z) of several complex variables z (p2) represented by a Dirichlet series, where M(x, F) = sup{¦F(x+iy¦: y p}, m(x, F) = inf{¦F(x+iy)¦: y p} (x, F) being the maximal term of the Dirichlet series, and x p.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 21–25. 相似文献
5.
Benjamin M. S. Martin 《Geometriae Dedicata》2001,86(1-3):19-27
Let be the fundamental group of a closed orientable surface of genus g 1, and let R(, G)/G be the space of conjugacy classes of representations of into a connected real reductive Lie group G. Motivated by the theory of geometric quantization, we define a map ¯ on R(, G)/G and investigate whether the fibres of ¯ are isotropic with respect to the natural symplectic structure on R(, G)/G. If g = 2 and G = SU(2), then the foliation given by the fibres of ¯ is equivalent to a real polarization defined by Weitsman, and we reprove his result that the fibres are isotropic in this case. If g = 1 then the fibres of ¯ are also isotropic, but we give an example to show that in general they are not. 相似文献
6.
L. D. Gogoladze 《Mathematical Notes》1972,11(2):93-96
It is proved that for anyf(x, y) L(R), where R=[-,,-, ], a function (x, y), exists such that ¦(x, y) ¦=¦f(x, y) ¦ for almost all (x, y) R. The Fourier series of the function (x, y) and all conjugate trigonometric series are A*-summable almost everywhere.Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 145–150, February, 1972. 相似文献
7.
We construct an infinite family{
n}n=5 of finite connected graphs
n that are multiple extensions of the well-known extended grid discovered in [1] (which is isomorphic to
5). The graphs
n are locally
n–1 forn > 5, and have the following property: the automorphism groupG(n) of
n permutes transitively the maximal cliques of
n (which aren-cliques) and the stabilizer of somen-clique of
n inG(n) induces
n on the vertices of. Furthermore we show that the clique complexes of the graphs
n are simply connected. 相似文献
8.
, , . , . Lip
The authors are indebted to Professor R. Bojanic for his valuable remarks and suggestions, especially for the simplification of the proof of Theorem 4. 相似文献
The authors are indebted to Professor R. Bojanic for his valuable remarks and suggestions, especially for the simplification of the proof of Theorem 4. 相似文献
9.
Joaquin Ortega 《Probability Theory and Related Fields》1982,59(2):169-177
Summary Let X={X(t), t
N} be a centred Gaussian random field with covariance X(t)X(s)=r(t–s) continuous on N×N and r(0)=1. Let (t,s)=((X(t)–X(s))
2)1/2; (t,s) is a pseudometric on N. Assume X is -separable. Let D
1 be the unit cube in N and for 0<k, D
k= {xN: k
–1
xD1}, Z(k)=sup{X(t),tD
k}. If X is sample continuous and ¦r(t)¦ =o(1/log¦t¦) as ¦t¦8 then Z(k)-(2Nlogk)
1/20 as k a.s. 相似文献
10.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1994,46(5):581-603
We study the minimality of elementsx
h,j,k
of canonical systems of root vectors. These systems correspond to the characteristic numbers
k
of operator functionsL() analytic in an angle; we assume that operators act in a Hilbert space
. In particular, we consider the case whereL()=I+T()c, >0,I is an identity operator,C is a completely continuous operator, (I- C)–1c for ¦arg¦, 0<<, the operator functionT() is analytic, and T()c for ¦arg¦<. It is proved that, in this case, there exists >0 such that the system of vectorsC
v
x
h,j,k
is minimal in
for arbitrary positive <1+, provided that ¦k¦>.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 545–566, May, 1994.This research was partially supported by the Ukrainian State Committee of Science and Technology. 相似文献
11.
Professor R. Ahlswede Professor J. Wolfowitz 《Probability Theory and Related Fields》1970,15(3):186-194
Summary Let X={1,..., a} be the input alphabet and Y={1,2} be the output alphabet. Let X
t
=X and Y
t
=Y for t=1,2,..., X
n
=
X
t
and Y
n
=
Y
t
. Let S be any set, C=={w(·¦·¦)s)¦sS} be a set of (a×2) stochastic matrices w(··¦s), and S
t=S, t=1,..., n. For every s
n
=(s
1,...,s
n
)
S
t
define P(·¦·¦s
n)=
w(y
t
¦x
t
¦s
t
) for every x
n=x
1, , x
nX
n and every y
n=(y
1, , y
n)Y
n. Consider the channel C
n
={P(·¦·¦)s
n
)¦s
n
S
n
} with matrices (·¦·¦s), varying arbitrarily from letter to letter. The authors determine the capacity of this channel when a) neither sender nor receiver knows s
n, b) the sender knows s
n, but the receiver does not, and c) the receiver knows s
n, but the sender does not.Research of both authors supported by the U.S. Air Force under Grant AF-AFOSR-68-1472 to Cornell University. 相似文献
12.
O. D. Tsereteli 《Mathematical Notes》1968,4(4):768-770
For any functionf of L(0, 2), we prove that there is a function L(0, 2) such that ¦(x)¦ = ¦f(x)¦ almost everywhere and L(0, 2), where is the conjugate of.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 461–465, October, 1968. 相似文献
13.
L. Kh. Burshtein 《Mathematical Notes》1969,6(4):705-709
Let a, a0, a, be a fixed point in the z-plane, (a, 0, ), the class of all systemsf
k()l
3 of functions z=f
k(), k=1, 2, 3, of which the first two map conformally and in a s ingle-sheeted manner the circle ¦¦<1, and the third maps in a similar manner the region ¦¦>1, into pair-wise nonintersecting regions Bk, k=1, 2, 3, containing the points a, 0, and , respectively, so thatf
1(0)=a,f
2(0)=0 andf
3()=. The region of values (a, 0, ) of the system M(¦f
1'(0)¦, ¦f
2'(0)¦, 1/¦f
3'()¦) in the class (a, 0, ) is determined.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 417–424, October, 1969. 相似文献
14.
F. G. Avkhadiev 《Mathematical Notes》1970,7(5):350-357
Strict upper bounds are determined for ¦s(z)¦, ¦Re s(z)¦, and ¦Im s(z) ¦ in the class of functions s(z)=a
nzn+an+1zn+1+... (n1) regular in ¦z¦<1 and satisfying the condition ¦u (1) –u (2) ¦K¦ 1-
2¦, where U()=Re s (ei
), K>0, and
1 and
2 are arbitrary real numbers. These bounds are used in the determination of radii of convexity and close-to-convexity of certain integral representations.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 581–592, May, 1970.The author wishes to thank L. A. Aksent'ev for his guidance in this work. 相似文献
15.
Let B be a domain in the complex plane, let pn(z) and Pn(z) be polynomials of degree n where the zeros of Pn(z) lie in
, let(z) be a finite function,(z) 0, z
. We consider the problem of estimating from above the functions L[pn(z)]=(z)pn(z) – wpn(z), z
, if ¦pn(z)¦ ¦Pn(z)¦ for zB. Under some very general conditions on B, z, (z), and w we prove the inequality ¦L[pn(z)]¦ ¦L[Pn(z)]¦.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 431–440, April, 1968. 相似文献
16.
E. P. Dolzhenko 《Mathematical Notes》1996,60(2):130-136
Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))2. LetH(x) be an arbitrary primitive of 1/h
–1(x). Note that the functionH
–1
x is positive and increasing on (–, +),H
–1 0 asx– andH
–1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000. 相似文献
17.
Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory 总被引:2,自引:0,他引:2
Let {X
k
, 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X
k
, 1 k n} and satisfying a
k
b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (max1 m n
k=1
m
k
X
k
> x) P (sum
k=1
n
k
X
k
> x) sum
k=1
n
P (
k
X
k
> x) hold as x . In doing so, no any assumption is made on the dependence structure of the sequence {
k
, 1 k n}. An application to ruin theory is proposed. 相似文献
18.
M. S. Sgibnev 《Mathematical Notes》1977,22(5):916-920
Let {n} be a sequence of identically distributed independent random variables,M1=<0,M
1
2
<;S
0=0,S
n
=1+2,+...+
n, n1;¯ S=sup {S
n
n=0.} The asymptotic behavior ofP(¯ St) as t is studied. If
t
P
(1x dx=0((t)), thenP(¯ St)– 1/¦¦
t
P (1x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks. 相似文献
19.
Summary In this note we observe that for independent symmetric random variables X and Y, when the pdf of X is PF, the conditional distributions of ¦Y¦ given S = X + Y form a MLR family. We then show that for a function : R
nR that is symmetric in each coordinate and increasing on (0, )n, E((S1,...,Sn)¦Sn = s) is even and increasing in ¦s¦. Here S1,...,Sn are partial sums with independent symmetric PF summands. Application is made to sequential tests that minimize the maximum expected sample size when the model is a one-parameter exponential family generated by a symmetric PF
density.Work supported by NSF grants MPS 72-05082 AO2 and MCS 75-23344 相似文献
20.
A. A. Gonchar 《Mathematical Notes》1972,11(2):83-86
For best piecewise polynomial approximation n=n (f; [0, 1]) of a functionf, which is continuous on the interval [0, 1] and admits a bounded analytic continuation onto the disk K=z:¦z–1¦<, the relation n=o[
f
(e
–n
)] is valid.Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 129–134, February, 1972. 相似文献