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1.
Here presented are two limit theorems for a kind of integrals involvingcomplex-valued functions of large numbers. The form of integrals may be regardedas a natural generalization of those integrals occured in the probability limit theoremsof Chung and Erds. Our main result is Theorem 2 whose Proof rests upon some knownresults of [1] and makes an extentive use of Bonnet's second mean value theorem andrelated analytic techniques. 相似文献
2.
GongZengtai 《数学研究》1994,27(1):77-82
In this paper, We give a varlational-type definition of (CnP) integrals. It is equivalent to the original definition of Perron-type and to the definition of Riemann-type, in this way the problem on definition of(CnP)′s Riemann-type has been solved completely. 相似文献
3.
Chaos decomposition of multiple integrals with respect to fractional Brownian motion (with H > 1/2) is given. Conversely the chaos components are expressed in terms of the multiple fractional integrals. Tensor product
integrals are introduced and series expansions in those are considered. Strong laws for fractional Brownian motion are proved
as an application of multiple fractional integrals.
Received: 22 September 1998 / Revised version: 20 April 1999 相似文献
4.
We establish limit theorems for integrals of shot-noise processes and study the asymptotic behavior of the moments of integrals of this type. 相似文献
5.
In this paper, we prove a central limit theorem for a sequence of multiple Skorokhod integrals using the techniques of Malliavin
calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences
of multiple stochastic integrals, and renormalized weighted Hermite variations of the fractional Brownian motion are discussed. 相似文献
6.
We introduce a generated Choquet integral with respect to absolutely monotone and sign stable set functions. Another type of integrals defined with respect to such a set function is obtained as a limit of an appropriate sequence of generated Choquet integrals. 相似文献
7.
用直接计算的方法对一类Hamilton系统的两个Abel积分比值的单调性进行讨论,指出该单词性条件可由两个判定函数直接确定. 相似文献
8.
We provide general conditions for normalized, time-scaled stochastic integrals of independently scattered, Lévy random measures
to converge to a limit. These integrals appear in many applied problems, for example, in connection to models for Internet
traffic, where both large scale and small scale asymptotics are considered. Our result is a handy tool for checking such convergence.
Numerous examples are provided as illustration. Somewhat surprisingly, there are examples where rescaling towards large times
scales yields a Gaussian limit and where rescaling towards small time scales yields an infinite variance stable limit, and
there are examples where the opposite occurs: a Gaussian limit appears when one converges towards small time scales and an
infinite variance stable limit occurs when one converges towards large time scales.
相似文献
9.
On a smooth closed surface, we consider integrals of the Cauchy type with kernel depending on the difference of arguments.
They cover both double-layer potentials for second-order elliptic equations and generalized integrals of the Cauchy type for
first-order elliptic systems. For the functions described by such integrals, we find sufficient conditions providing their
continuity up to the boundary surface. We obtain the corresponding formulas for their limit values. 相似文献
10.
Bernard Bialecki 《Numerische Mathematik》1990,57(1):263-269
Summary A Sinc quadrature rule is presented for the evaluation of Hadamard finite-part integrals of analytic functions. Integration over a general are in the complex plane is considered. Special treatment is given to integrals over the interval (–1,1). Theoretical error estimates are derived and numerical examples are included. 相似文献
11.
We present some basic identities for hypergeometric functions associatedwith the integrals of Euler type. We give a geometrical proof for formulaesuch as the identity between the single and double integrals expressingAppell's hypergeometric series F1 (a, b, b' c; x, y). 相似文献
12.
Dominika Bogusz 《Journal of Optimization Theory and Applications》2013,156(3):650-682
We consider an infinite-horizon optimal control problem with the cost functional described either by an integral over an unbounded interval (a Lebesgue integral) or by a limit of integrals (an improper Lebesgue integral). We prove some theorems on the existence of solutions to such problems. The proofs are based on appropriate lower closure theorems and some extensions of Olech’s theorem on the lower semicontinuity of an integral functional; these extensions cover the cases of functionals described by an integral over an unbounded interval and by a limit of integrals. 相似文献
13.
14.
Multiple fractional integrals 总被引:2,自引:0,他引:2
Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly
identified.
Received: 23 February 1998 / Revised version: 31 July 1998 相似文献
15.
We consider a multiple-integral representation for a one-parameter generating function of the finite temperature Sz-Sz correlation functions of the antiferromagnetic spin-1/2 XXZ chain in the XX limit and in the Ising limit. We show how the
multiple integrals reduce to single integrals in these limits, thus reproducing known results.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 146–160, January, 2006. 相似文献
16.
Erik G.F. Thomas 《Probability Theory and Related Fields》2001,119(4):579-588
In this paper we prove, for signed or complex Radon measures on completely regular spaces, the analogue of Prokhorov's criterion
on the existence of the projective limit of a compatible system of measures. Because of loss of mass under projections this
cannot be reduced to the case of positive measures. Countable projective limits are, as in the case of positive measures,
particularly simple, the sole condition now being the boundedness of the total variations. It is shown, with the help of the
martingale convergence theorem, that the densities of these complex measures with respect to their variations, converge in
an appropriate sense. This work is part of an extended project on the mathematical theory of path integrals.
Received: 18 June 1997 / Revised version: 11 August 2000/?Published online: 9 March 2001 相似文献
17.
Liudas Giraitis Murad S. Taqqu Norma Terrin 《Probability Theory and Related Fields》1998,110(3):333-367
Summary. Let (X
t
,t∈Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low frequencies. This
includes situations, known as strong (or long-range) dependence, where the spectral density diverges at the origin. We study
quadratic forms of bivariate Appell polynomials of the sequence (X
t
) and provide general conditions for these quadratic forms, adequately normalized, to converge to a non-Gaussian distribution.
We consider, in particular, circumstances where strong and weak dependence interact. The limit is expressed in terms of multiple
Wiener-It? integrals involving correlated Gaussian measures.
Received: 22 August 1996 / In revised form: 30 August 1997 相似文献
18.
Ya. A. Butko 《Journal of Mathematical Sciences》2008,151(1):2629-2638
A solution of the Cauchy-Dirichlet problem is represented as the limit of a sequence of integrals over finite Cartesian powers
of the domain of the manifold considered. It is shown that these limits coincide with the integrals with respect to surface
measures of Gauss type on the set of trajectories in the manifold. Moreover, the integrands are a combination of elementary
functions of the coefficients of the equation considered and geometric characteristics of the manifold. Also, a solution of
the Cauchy-Dirichlet problem in the domain of the manifold is represented as the limit of a solution of the Cauchy problem
for the heat equation on the whole manifold under an infinite growth of the absolute value of the potential outside the domain.
The proof uses some asymptotic estimates for Gaussian integrals over Riemannian manifolds and the Chernoff theorem.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 3–15, 2006. 相似文献
19.
G. F. Bryant 《Journal of Optimization Theory and Applications》1976,18(2):285-289
Developments and generalizations of a theorem of Halkin, on the limit of the multiple balayage of vector integrals, are deduced via Riemann integration theory. 相似文献
20.
Naoto Kumano-go 《Bulletin des Sciences Mathématiques》2004,128(3):197-251
Using the time slicing approximation, we give a mathematically rigorous definition of Feynman path integrals for a general class of functionals on the path space. As an application, we prove the interchange with Riemann-Stieltjes integrals, the interchange with a limit, the perturbation expansion formula, the semiclassical approximation, and the fundamental theorem of calculus in Feynman path integral. 相似文献