共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
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
3.
M. J. Grimble 《Journal of Optimization Theory and Applications》1978,26(3):427-451
In the development of a roll force model for cold rolling, techniques were developed for solving the system equations which are of general interest. This paper gives a brief introduction to the physical model but concentrates on the solution of the model equations and the simulation. An unusual feature of the model was that the calculated profiles had to satisfy a number of boundary conditions at different points throughout the roll arc. A new method was developed for calculating these profiles and for determining the gradient functions which satisfied the boundary constraints.Nomenclature
p()
pressure at roll angle
-
h()
gauge
-
a()
roll radius
-
y()
yield stress
-
g
i
()
gradient function on iterationi
-
e()
gauge error
- (, )
transition function
-
H(–)
Heaviside unit step function at =
-
(–)
unit impulse function at =
-
H(,
1,
2)
defined asH( –
1) –H( –
2)
-
angular position from the roll center line
-
T
angular limits of roll arc represented
-
n
angular position of the neutral angle
-
i
angular position ofith strip elastic-plastic boundary
-
pi
pressure change at the boundaryi
-
i
,
i
,
i
constants defined in Appendix A
-
k
1,k
2
elastic region constants
-
k
total number of strip boundaries (elastic-plastic and entry and exit points)
-
R
undeformed work roll radius
-
R
s
roll separation—distance between roll centers
-
h
01
unstrained gauge in an elastic region
-
h
in
gauge of the strip at the entry to the roll gap
-
J
gauge error cost function
- <x, y>
inner product ofx andy
- x
norm ofx
-
L
2[0,
T
]
the space of Lebesgue square-integrable functions defined on the interval [0,
T
]
- JUVY
denotes (Dx)() =dx()/d
The author would like to acknowledge the help given by Dr. G. F. Bryant, Director, and Mr. M. A. Fuller, Senior Research Engineer, the Industrial Automation Group, Imperial College of Science and Technology, London. He is also grateful to M. J. G. Henderson of the University of Birmingham for his advice and encouragement during the project. He would like to thank the Directors of GEC Electrical Projects Limited for allowing him to undertake the work and also Mr. J. McTaggart and Mr. C. McKenzie (GEC), Professor H. A. Prime of the University of Birmingham, and Dr. G. F. Bryant for arranging the project. 相似文献
4.
M. Menéndez D. Morales L. Pardo I. Vajda 《Annals of the Institute of Statistical Mathematics》2001,53(2):277-288
The paper considers statistical models with real-valued observations i.i.d. by F(x, 0) from a family of distribution functions (F(x, ); ), R
s
, s 1. For random quantizations defined by sample quantiles (F
n
–1 (1),, F
n
–1 (
m–1)) of arbitrary fixed orders 0 < 1 < m-1 < 1, there are studied estimators ,n
of 0 which minimize -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F
–1 (1,0),, F
–1 (
m–1, 0)). Moreover, the Fisher information matrix I
m
(0, ) of the latter model with the equidistant orders = (
j
= j/m : 1 j m – 1) arbitrarily closely approximates the Fisher information J(0) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type. 相似文献
5.
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
6.
Cheng -Tan Hsiao 《Probability Theory and Related Fields》1982,59(1):39-53
Summary LetU(x), x
d-|0}, be a nonnegative even function such that x
0U(x)1. In this paper, we consider an infinite system of stochastic process
t
(x); x
d with the following mechanism: at each sitex, after mean 1 exponential waiting time,
t(x) is replaced by a Gaussian random variable with mean
yx
t
(y) U(y-x) and variance 1. It is understood here that all the interactions are independent of one another. The behavior of this system will be investigated and some ergodic theorems will be derived. The results strongly depend whether
x
0
U(x)<1 or =1. 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.
Paul Trow 《Monatshefte für Mathematik》1998,125(2):165-172
We describe all possible decompositions of a finite-to-one factor map :
A
S, from an irreducible shift of finite type onto a sofic shift, into two maps =, such that the range of is a shift of finite type, and is bi-closing. We also give necessary and sufficient conditions for to be almost topologically conjugate overS to a bi-closing map. 相似文献
9.
M. B. Korobkova 《Mathematical Notes》1972,11(3):158-162
In the present note a theorem about strong suitability of the space of algebraic polynomials of degree n in C[a,b] (Theorem A in [1]) is generalized to the space of spline polynomials
[a, b
]n, k
(n2, 0) in C[a, b]. Namely, it is shown that the following theorem is valid: for arbitrary numbers 0, 1, ..., n+k, satisfying the conditions (i–i–1) (i+1{
i< 0(i=1, ..., n +k–1), there is a unique polynomials
n,k (t)
[a, b
]/n,k
and pointsa=0,<1<...<
n+k– 1<
n+k = b (11 <n, ..., kk<n+k–1), such that sn,k(i) = i(i=0, ..., n + k), sn,k(i)=0 (i=1, ..., n + k–1).Translated from Matematicheskii Zametki, Vol. 11, No. 3, pp. 251–258, March, 1972. 相似文献
10.
A. V. Ivanov 《Mathematical Notes》1976,20(2):721-727
A nonlinear regression modelx
t=gt(0)+ t,t1, is considered. Under a number of conditions on its elements t and gt(0) it is proved that the distribution of the normalized least square estimate of the parameter 0 converges uniformly on the real axis to the standard normal law at least as quickly as a quantity of the order T–1/2 as T , where T is the size of the sample, by which the estimate is formed.Translated from Matematicheskie Zametki, Vol. 20, No. 2, pp. 293–303, August, 1976. 相似文献
11.
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
12.
I. A. Ibragimov 《Journal of Mathematical Sciences》1982,20(3):2164-2175
Let be a Gaussian random vector with values in a Hilbert space H. We denote by(a, z) the ball in H with center ata and of radius z. Some asymptotic formulas for I (a, z)=P (a, z), z 0, are presented in the paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 75–93, 1979. 相似文献
13.
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
14.
15.
Ole Barndorff-Nielsen 《Probability Theory and Related Fields》1969,12(1):56-58
Summary Let P={P
: } be an exponential family of probability distributions with the canonical parameter and consider the one to one mapping : P
. It is shown that, under mild regularity assumptions, and
–1 are continuous with respect to the Lévy metric in P and Euclidean metric in . 相似文献
16.
Moshe Shaked J. George Shanthikumar 《Annals of the Institute of Statistical Mathematics》1990,42(3):509-531
A collection of random variables {X(), } is said to be parametrically stochastically increasing and convex (concave) in if X() is stochastically increasing in , and if for any increasing convex (concave) function , E(X()) is increasing and convex (concave) in whenever these expectations exist. In this paper a notion of directional convexity (concavity) is introduced and its stochastic analog is studied. Using the notion of stochastic directional convexity (concavity), a sufficient condition, on the transition matrix of a discrete time Markov process {X
n(), n=0,1,2,...}, which implies the stochastic monotonicity and convexity of {X
n(), }, for any n, is found. Through uniformization these kinds of results extend to the continuous time case. Some illustrative applications in queueing theory, reliability theory and branching processes are given.Supported by the Air Force Office of Scientific Research, U.S.A.F., under Grant AFOSR-84-0205. Reproduction in whole or in part is permitted for any purpose by the United States Government. 相似文献
17.
A Comparison of Methods for Estimating the Extremal Index 总被引:1,自引:0,他引:1
The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements. 相似文献
18.
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
19.
A. M. Kagan 《Journal of Mathematical Sciences》1986,34(2):1482-1487
Summary Denote by
k
a class of familiesP={P} of distributions on the line R1 depending on a general scalar parameter , being an interval of R1, and such that the moments µ1()=xdP
,...,µ2k
()=x
2k
dP
are finite, 1 (), ..., k (), k+1 () ...,
k
() exist and are continuous, with 1 () 0, and
j
+1 ()= 1 ()
j
() +[2() -1()2]
j
()/ 1 (), J=2, ..., k. Let 1=¯x=x
1 + ... +x
n/n, 2=x
1
2 + ... +x
n
2/n, ...,
k
=(x
1
k
+ ... +x
n
k/n denote the sample moments constructed for a sample x1, ..., xn from a population with distribution Pg. We prove that the estimator of the parameter by the method of moments determined from the equation 1= 1() and depending on the observations x1, ..., xn only via the sample mean ¯x is asymptotically admissible (and optimal) in the class
k
of the estimators determined by the estimator equations of the form 0 () + 1 () 1 + ... +
k
()
k
=0 if and only ifP
k
.The asymptotic admissibility (respectively, optimality) means that the variance of the limit, as n (normal) distribution of an estimator normalized in a standard way is less than the same characteristic for any estimator in the class under consideration for at least one 9 (respectively, for every ).The scales arise of classes
1
2... of parametric families and of classes 1 2 ... of estimators related so that the asymptotic admissibility of an estimator by the method of moments in the class
k
is equivalent to the membership of the familyP in the class
k
.The intersection consists only of the families of distributions with densities of the form h(x) exp {C0() + C1() x } when for the latter the problem of moments is definite, that is, there is no other family with the same moments 1 (), 2 (), ...Such scales in the problem of estimating the location parameter were predicted by Linnik about 20 years ago and were constructed by the author in [1] (see also [2, 3]) in exact, not asymptotic, formulation.Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, pp. 41–47, 1981. 相似文献
20.
Like dismantling for finite posets, a perfect sequence = P
: of a chain complete posetP represents a canonical procedure to produce a coreP
. It has been proved that if the posetP contains no infinite antichain then this coreP
is a retract ofP andP has the fixed point property iffP
has this property. In this paper the condition of having no infinite antichain is replaced by a weaker one. We show that the same conclusion holds under the assumption thatP does not contain a one-way infinite fence or a tower.Supported by a grant from The National Natural Science Foundation of China. 相似文献