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1.
In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L p , to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.  相似文献   

2.
 In this report we detail the following story. Several centuries ago, Abel noticed that the well-known elementary integral
is just an augur of more surprising integrals of the shape
Here f is a polynomial of degree g and the D are certain polynomials of degree deg . Specifically, (so q divides ). Note that, morally, one expects such integrals to produce inverse elliptic functions and worse, rather than an innocent logarithm of an algebraic function. Abel went on to study, well, abelian integrals, and it is Chebychev who explains – using continued fractions – what is going on with these ‘quasi-elliptic’ integrals. Recently, the second author computed all the polynomials D over the rationals of degree 4 that have an f as above. We will explain various contexts in which the present issues arise. Those contexts include symbolic integration of algebraic functions; the study of units in function fields; and, given a suitable polynomial g, the consideration of period length of the continued fraction expansion of the numbers as n varies in the integers. But the major content of this survey is an introduction to period continued fractions in hyperelliptic – thus quadratic – function fields. (Received 7 December 1999; in revised form 29 April 2000)  相似文献   

3.
Ifh denotes the product of finitely many concave non-negative functions on a compact interval [a, b], then it is shown that there exist pointsα andβ withaαβb such thath is strictly increasing on [α, α), constant on (α, β), and strictly decreasing on (β, b]. This structure theorem leads to an extension of several classical optimization results for concave functions on convex sets to the case of products of concave functions.  相似文献   

4.
Stochastic differential equations in ?n with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space Wβ2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution procedure is developed which combines the stochastic Itô calculus with fractional calculus via norm estimates of associated integral operators in Wα 2 for 0 < α < 1. Linear equations are considered as a special case. This approach leads to fast computer algorithms basing on Picard's iteration method. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
A question of Yves Meyer motivated the research concerning “time” subordinations of real functions. Denote by B1a{\mathcal {B}}_{1}^{\alpha} the metric space of functions with Lipschitz constant 1 defined on [0,1], equipped with the complete metric defined via the supremum norm. Given a function g ? B1ag\in {\mathcal {B}}_{1}^{\alpha} one obtains a time subordination of g simply by considering the composite function Z=gf, where f∈ℳ:={f:f(0)=0, f(1)=1 and f is a continuous nondecreasing function on [0,1]}. The metric space Ea=M×B1a\mathcal {E}^{\alpha}=\mathcal {M}\times {\mathcal {B}}_{1}^{\alpha} equipped with the product supremum metric is a complete metric space. In this paper for all α∈[0,1) multifractal properties of gf are investigated for a generic (typical) element (f,g)∈ℰ α . In particular we determine the generic H?lder singularity spectrum of gf.  相似文献   

6.
A Cohen-Macaulay complex is said to be balanced of typea=(a 1,a 2, ...,a s ) if its vertices can be colored usings colors so that every maximal face gets exactlya i vertices of thei:th color. Forb=(b 1,b 2, ...,b s ), 0≦ba, letf b denote the number of faces havingb i vertices of thei:th color. Our main result gives a characterization of thef-vectorsf=(f b )0≦ba or equivalently theh-vectors, which can arise in this way from balanced Cohen-Macaulay complexes. As part of the proof we establish a generalization of Macaulay’s compression theorem to colored multicomplexes. Finally, a combinatorial shifting technique for multicomplexes is used to give a new simple proof of the original Macaulay theorem and another closely related result. First and third authors partially supported by the National Science Foundation.  相似文献   

7.
We discuss the Grüss inequalities on spaces of continuous functions defined on a compact metric space. Using the least concave majorant of the modulus of continuity, we obtain the Grüss inequality for the functional L(f) = H(f; x), where H:C[a, b] → C[a, b] is a positive linear operator and x ∈ [a, b] is fixed. We apply this inequality in the case of known operators, e.g., the Bernstein operator, the Hermite–Fejér interpolation operator, and convolution-type operators. Moreover, we deduce Grüss-type inequalities using the Cauchy mean-value theorem, thus generalizing results of Chebyshev and Ostrowski. The Grüss inequality on a compact metric space for more than two functions is given, and an analogous Ostrowski-type inequality is obtained. The latter, in turn, leads to one further version of the Grüss inequality. In the appendix, we prove a new result concerning the absolute first-order moments of the classic Hermite–Fejér operator.  相似文献   

8.
On a Multiple Stratonovich-type Integral for Some Gaussian Processes   总被引:2,自引:0,他引:2  
We construct a multiple Stratonovich-type integral with respect to Gaussian processes with covariance function of bounded variation. This construction is based on the previous definition of the multiple Itô-type integral given by Huang and Cambanis [Ann. Propab. 6(4), 585–614] and on a Hu–Meyer formula (that is, an expression of the multiple Stratonovich integral as a sum of Itô-type integrals of inferior or equal order) for the elementary functions. We also apply our results to the fractional Brownian motion with Hurst parameter $H > \frac{1}{2}We construct a multiple Stratonovich-type integral with respect to Gaussian processes with covariance function of bounded variation. This construction is based on the previous definition of the multiple It?-type integral given by Huang and Cambanis [Ann. Propab. 6(4), 585–614] and on a Hu–Meyer formula (that is, an expression of the multiple Stratonovich integral as a sum of It?-type integrals of inferior or equal order) for the elementary functions. We also apply our results to the fractional Brownian motion with Hurst parameter .  相似文献   

9.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}The aim of this study is to prove global existence of classical solutions for systems of the form \frac?u?t -a Du=-f(u,v){\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)} , \frac?v?t -b Dv=g(u,v){\frac{\partial v}{\partial t} -b \Delta v=g(u,v)} in (0, +∞) × Ω where Ω is an open bounded domain of class C 1 in \mathbbRn{\mathbb{R}^n}, a > 0, b > 0 and f, g are nonnegative continuously differentiable functions on [0, +∞) × [0, +∞) satisfying f (0, η) = 0, g(x,h) £ C j(x)eahb{g(\xi,\eta) \leq C \varphi(\xi)e^{\alpha {\eta^\beta}}} and g(ξ, η) ≤ ψ(η)f(ξ, η) for some constants C > 0, α > 0 and β ≥ 1 where j{\varphi} and ψ are any nonnegative continuously differentiable functions on [0, +∞) such that j(0)=0{\varphi(0)=0} and limh? +¥hb-1y(h) = l{ \lim_{\eta \rightarrow +\infty}\eta^{\beta -1}\psi(\eta)= \ell} where is a nonnegative constant. The asymptotic behavior of the global solutions as t goes to +∞ is also studied. For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates and Lyapunov functional methods.  相似文献   

10.
The standard routine QAGE from Quadpack is modified to allow the efficient evaluation of integrals of the form a b gf(x)¦)dx, wheref andg are assumed to be smooth. Using function values available during the adaptive integration process, zeros off are found and used as subdivision points. The technique compares favourably with both the original bisection strategy and the nonuniform trisection strategy of Berntsen et al. The modified algorithm extends the class of integrals that can be integrated with an automatic code, since it copes with problem integrals that can not be integrated using the bisection or trisection strategies.  相似文献   

11.
 We extend the mean-value theorems for multiplicative functions f on additive arithmetic semigroups, which satisfy the condition ∣f(a)∣≤1, to a wider class of multiplicative functions f for which ∣f(a)∣ is bounded in some average sense, via Halász’s method in classical probabilistic number theory.  相似文献   

12.
We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the Skorohod integral deduced from It?'s formula for this anticipating stochastic integral. Received: 21 November 1997 / Revised version: 20 July 1998  相似文献   

13.
In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [J.G. Gimbel and A.N. Trenk, On the weakness of an ordered set, SIAM J. Discrete Math. 11 (1998) 655-663; P.J. Tanenbaum, A.N. Trenk, P.C. Fishburn, Linear discrepancy and weak discrepancy of partially ordered sets, ORDER 18 (2001) 201-225; A.N. Trenk, On k-weak orders: recognition and a tolerance result, Discrete Math. 181 (1998) 223-237]. The fractional weak discrepancywdF(P) of a poset P=(V,?) is the minimum nonnegative k for which there exists a function f:VR satisfying (1) if a?b then f(a)+1?f(b) and (2) if ab then |f(a)-f(b)|?k. We formulate the fractional weak discrepancy problem as a linear program and show how its solution can also be used to calculate the (integral) weak discrepancy. We interpret the dual linear program as a circulation problem in a related directed graph and use this to give a structural characterization of the fractional weak discrepancy of a poset.  相似文献   

14.
讨论了一类带分数Brown 运动的非Lipschitz 增长的随机微分方程适应解的存在唯一性。关于分数 Brown 运动的随机积分有多种定义,本文使用一种广义 Stieltjes积分定义方法,利用这种积分的性质,建立了一类由标准 Brown 运动和一个 Hurst 指数H ∈(1/2,1)的分数Brown 运动共同驱动的、系数为非Lipschitz 增长的随机微分方程适应解的存在唯一性定理。  相似文献   

15.
A general weighted integral inequality for two continuous functions on an interval [a,b] is presented. The equality conditions are given. This result implies the new inequalities for the incomplete beta and gamma functions as well as the related estimates for the confluent hypergeometric function, error function, and Dawson's integral. Also it implies various weighted integro-differential inequalities, those of the Opial type included, and some inequalities which involve the Erdélyi–Kober and Riemann–Liouville fractional integrals.  相似文献   

16.
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   

17.
We study the boundedness of generalized multilinear fractional integrals. An O’Neil type inequality for a k-linear integral operator is proved. Using an O’Neil type inequality for a k-linear integral operator, we obtain a pointwise rearrangement estimate of generalized multilinear fractional integrals. By way of application we prove a Sobolev type theorem for these integrals. __________ Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 577–585, May–June, 2007.  相似文献   

18.
In this paper, we will prove the existence of infinitely many harmonic and subharmonic solutions for the second order differential equation g(x) = f(t, x) using the phase plane analysis methods and Poincaré–Birkhoff Theorem, where the nonlinear restoring field g exhibits superlinear conditions near the infinity and strong singularity at the origin, and f(t, x) = a(t)x γb(t, x) where 0 ≤ γ ≤ 1 and b(t, x) is bounded.  相似文献   

19.
 We extend the mean-value theorems for multiplicative functions f on additive arithmetic semigroups, which satisfy the condition ∣f(a)∣≤1, to a wider class of multiplicative functions f for which ∣f(a)∣ is bounded in some average sense, via Halász’s method in classical probabilistic number theory. Received October 18, 2001; in final form April 11, 2002  相似文献   

20.
In this paper we use the theory of normal families to prove: Let a and b be two complex numbers such that ba, 0, and let f be a non-constant entire function. If f and f′ share the value a CM and if f = b whenever f′ = b, then ff′. This result improves a result due to Rubel and Yang. Received: 13 June 2005  相似文献   

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