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1.
B. A. Sevast'yanov 《Mathematical Notes》1968,3(4):247-251
Conditions are found which must be imposed on a function g(x) in order that M g(1+2+ + v < if M g(i) < and M g(v) < ,, 1, 2, , n, ... being non-negative and independent, being integral, and {i} being identically distributed. The result is applied to the theory of branching processes.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 387–394, April, 1968. 相似文献
2.
3.
G. U. Mynbaeva 《Ukrainian Mathematical Journal》1994,46(10):1573-1577
We study the rate of convergence of the process(tT)/T to the processw(t)/ asT , where(t) is a solution of the stochastic differential equationd(t)=a((t))dt+((t))dw(t)
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1424–1427, October, 1994. 相似文献
4.
B. Barabás 《Periodica Mathematica Hungarica》1987,18(2):115-122
The properties of the empirical density function,f
n(x) = k/n(
j
+
–
j-1
+
) if
j-1
+
< x + where
j-1
+
and
j
+
are sample elements and there are exactlyk – 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a good estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions. 相似文献
5.
A. V. Pazhitnov 《K-Theory》1996,10(4):323-412
Let M be a closed connected smooth manifold with dim M=n6, and :
1(M) Z be an epimorphism. Denote by the group ring of
1(M) and let
–
be its Novikov completion. Let D
* be a free-based finitely generated chain complex over
–
. Assume that D
ii=0 for i1 and in–1 and that D
* has the same simple homotopy type as the Novikov-completed simplicial chain complex of the universal covering M. Let N be an integer. We prove that D
* can be realized, up to the terms of
–
of degree N as the Novikov complex of a Morse map : M S
1, belonging to . Applications to Arnold's conjectures and to the theory of fibering of M over S
1 are given. 相似文献
6.
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
7.
J. C. Dunn 《Journal of Optimization Theory and Applications》1987,55(2):203-216
The projected gradient methods treated here generate iterates by the rulex
k+1=P
(x
k
–s
k
F(x
k
)),x
1 , where is a closed convex set in a real Hilbert spaceX,s
k
is a positive real number determined by a Goldstein-Bertsekas condition,P
projectsX into ,F is a differentiable function whose minimum is sought in , and F is locally Lipschitz continuous. Asymptotic stability and convergence rate theorems are proved for singular local minimizers in the interior of , or more generally, in some open facet in . The stability theorem requires that: (i) is a proper local minimizer andF grows uniformly in near ; (ii) –F() lies in the relative interior of the coneK
of outer normals to at ; and (iii) is an isolated critical point and the defect P
(x – F(x)) –x grows uniformly within the facet containing . The convergence rate theorem imposes (i) and (ii), and also requires that: (iv)F isC
4 near and grows no slower than x–4 within the facet; and (v) the projected Hessian operatorP
F
2
F()F
is positive definite on its range in the subspaceF
orthogonal toK
. Under these conditions, {x
k
} converges to from nearby starting pointsx
1, withF(x
k
) –F() =O(k
–2) and x
k
– =O(k
–1/2). No explicit or implied local pseudoconvexity or level set compactness demands are imposed onF in this analysis. Furthermore, condition (v) and the uniform growth stipulations in (i) and (iii) are redundant in
n
. 相似文献
8.
Olav Kallenberg 《Probability Theory and Related Fields》1980,52(2):127-147
Summary The present paper continues the work by Davidson, Krickeberg, Papangelou, and the author on proving, under weakest possible assumptions, that a stationary random measure or a simple point process on the space of k-flats in R
d
is a.s. invariant or a Cox process respectively. The problems for and are related by the fact that is Cox whenever the Papangelou conditional intensity measure of (a thinning of) is a.s. invariant. In particular, is shown to be a.s. invariant, whenever it is absolutely continuous with respect to some fixed measure and has no (so called) outer degeneracies. When k=d–22, no absolute continuity is needed, provided that the first moments exist and that has no inner degeneracies either. Under a certain regularity condition on , it is further shown that and are simultaneously non-degenerate in either sense. 相似文献
9.
We study 3---manifolds having Q parallel to characteristic field and the scalar curvature constant along the geodesic foliation generated by e or e. We find out a new class of contact metric 3-manifolds and we give non-flat examples of this class. 相似文献
10.
René L. Schilling 《Journal of Theoretical Probability》1998,11(2):303-330
Let {X
t}
t0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇn|q(Ç,)|c(1=)()) for some fixed continuous negative definite function (). The Hausdorff dimension of the set {X
t:tE}, E [0, 1] is any analytic set, is a.s. bounded above by dim E. is the Blumenthal–Getoor upper index of the Levy Process associated with (). 相似文献
11.
Wenbo V. Li 《Journal of Theoretical Probability》1992,5(1):1-31
Let =(
n
) be i.i.d.N(0, 1) random variables andq(x), q(x):R
[0, ) be seminorms. We investigate necessary and sufficient conditions that the ratio ofP(q()<) andP(q()<) goes to a positive constant as 0+. We give satisfactory answers forl
2-norms and also some results for sup-norms andl
p-norms. Some applications are given to the rate of escape of infinite dimensional Brownian motion, and we give the lower tail of the Ornstein-Uhlenbeck process and a weighted Brownian bridge under theL
2-norms. 相似文献
12.
Fan Xianling 《数学学报(英文版)》1996,12(3):254-261
In this paper the regularity of the Lagrangiansf(x, )=||(x)(1<
1(x)2< +) is studied. Our main result: If(x) is Holder continuous, then the Lagrangianf(x, )=f(x, )=||(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.Supported by the National Natural Science Foundation of China. 相似文献
13.
Zusammenfassung Es wird die Spannungsverteilung untersucht, die sich in einem breiten Balken mit konstanter Höhe unter einem konstanten Biegemoment ausbildet, wenn er eine kleine elliptische Einschliessung mit Zentrum auf der Neutralachse enthält. Insbesondere werden die Fälle eines sehr starren Einschlusses sowie eines elliptischen Loches im Detail diskutiert.
Nomenclature x, y Cartesian coordinates - , elliptic coordinates - u, v (u ,u )=components of displacements - , unit elongations in -and -directions - shearing strain - , normal stress components in elliptical coordinates - shearing stress in elliptic coordinates - x , y normal stress in Cartesian coordinates - xy shearing stress in Cartesian coordinates - E Young's modulus for the beam - v Poisson's ratio for the beam - 1/h 1, 1/h 2 stretch ratios - e x + y dilatation - 2 rotation - M bending moment 相似文献
Nomenclature x, y Cartesian coordinates - , elliptic coordinates - u, v (u ,u )=components of displacements - , unit elongations in -and -directions - shearing strain - , normal stress components in elliptical coordinates - shearing stress in elliptic coordinates - x , y normal stress in Cartesian coordinates - xy shearing stress in Cartesian coordinates - E Young's modulus for the beam - v Poisson's ratio for the beam - 1/h 1, 1/h 2 stretch ratios - e x + y dilatation - 2 rotation - M bending moment 相似文献
14.
We prove a local limit theorem (LLT) on Cramer-type large deviations for sums S
V
=
t
V (
t
), where
t
, t Z
, 1, is a Markov Gaussian random field, V Z
, and is a bounded Borel function. We get an estimate from below for the variance of S
V
and construct two classes of functions , for which the LLT of large deviations holds. 相似文献
15.
Takashi Hara 《Probability Theory and Related Fields》1990,86(3):337-385
Summary Extending the method of [27], we prove that the corrlation length of independent bond percolation models exhibits mean-field type critical behaviour (i.e. (p(p
c
–p)–1/2 aspp
c
) in two situations: i) for nearest-neighbour independent bond percolation models on ad-dimensional hypercubic lattice
d
, withd sufficiently large, and ii) for a class of spread-out independent bond percolation models, which are believed to belong to the same universality class as the nearest-neighbour model, in more than six dimensions. The proof is based on, and extends, a method developed in [27], where it was used to prove the triangle condition and hence mean-field behaviour of the critical exponents , , , and 2 for the above two cases. 相似文献
16.
G. I. Ivanova 《Journal of Mathematical Sciences》1991,57(4):3240-3241
We are considering the problem of controlling a one-dimensional Wiener process (t) (0)=0,E=0,D=
2t.Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei. Trudy Seminara, 1988, pp. 53–55. 相似文献
17.
G. M. Feldman 《Journal of Theoretical Probability》2004,17(4):929-941
It is well-known Heyde's characterization theorem for the Gaussian distribution on the real line: if
j
are independent random variables,
j
,
j
are nonzero constants such that
i
±
j
–1
j
0 for all i j and the conditional distribution of L
2=1 1 + ··· +
n
n
given L
1=1 1 + ··· +
n
n
is symmetric, then all random variables
j
are Gaussian. We prove some analogs of this theorem, assuming that independent random variables take on values in a finite Abelian group X and the coefficients
j
,
j
are automorphisms of X. 相似文献
18.
For every ordinal <1 we define a new type of convergence for sequences of functions (-uniform pointwise) which is intermediate between uniform and pointwise convergence. Using this type of convergence we obtain an Egorov type theorem for sequences of measurable functions. 相似文献
19.
We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d
t
=db
t
+T(
t
)dt with the initial data 0=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C
B
consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d
t
=
db
t
+
t
dt
with initial data 0=0, where ,R,0 and 0<. 相似文献
20.
We give a classification of 3—dimensional conformally flat contact metric manifolds satisfying: =0(=L
g) orR(Y, Z)=k[(Z)Y–(Y)Z]+[(Z)hY]–(Y)hZ] wherek and are functions. It is proved that they are flat (the non-Sasakian case) or of constant curvature 1 (the Sasakian case). 相似文献