共查询到20条相似文献,搜索用时 31 毫秒
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随机1-集压缩算子的随机不动点指数和随机不动点定理 总被引:24,自引:0,他引:24
在[1]中我们建立了随机拓扑度并得到系列新的随机不动点定理,本文建立了随机1-集压缩算子的随机不动点指数理论,得到一些新的随机不动点定理,为研究各类随机方程提供一些存在性原理,给出了在随机Hammerstein积分方程的应用. 相似文献
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殷承元 《纯粹数学与应用数学》2013,(3):221-225
在轨迹二阶导数具有Hlder连续的条件下,利用高阶奇异积分思想和概率极限的理论,研究了在Brown运动下的随机奇异积分.得到了以Brown运动为积分元的随机奇异积分是存在性定理. 相似文献
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胡耀忠 《数学物理学报(B辑英文版)》2010,(6):2033-2050
In this paper we study the integral curve in a random vector field perturbed by white noise. It is related to a stochastic transport-diffusion equation. Under some conditions on the covariance function of the vector field, the solution of this stochastic partial differential equation is proved to have moments. The exact p-th moment is represented through integrals with respect to Brownian motions. The basic tool is Girsanov formula. 相似文献
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Kahane Jean-Pierre 《数学年刊B辑(英文版)》1987,8(1):1-12
Given Q_n(t) (n=0, 1,\cdots), a positive martingale indexed by t (t\in T, compact metric space) and a measure \sigma \in M^+(T), the random measure Q\sigma is defined as a limit of Q_n\sigma. In general EQ\sigma \leq \sigma. Conditions are given to insure either EQ\sigma=0 (degeneracy) or EQ\sigma=\sigma(full action). In the particular case when Q_n(t) a product of independent weight functions,\sigma is decomposed into a sum of two mutually singular measures,\sigma=\sigma''+\sigma'', such that Q acts fully on \sigma'' and is degeneoate on \sigma'', and the operator EQ is a projection. Examples and applications aoe given (random covecings, B. Mandelbrot''s martingales, multiplicative chaos). 相似文献
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T Burczyński 《Applied Mathematical Modelling》1985,9(3):189-194
Stochastic Dirichlet and Neumann boundary value problems and stochastic mixed problems have been formulated. As a result the stochastic singular integral equations have been obtained. A way of solving these equations by means of discretization of a boundary using stochastic boundary elements has been presented, resulting in a set of random algebraic equations. It has been proved that for Dirichlet and Neumann problems probabilistic characteristics (i.e. moments: expected value and correlation function) fulfilled deterministic singular integral equations. A numerical method of evaluation of moments on a boundary and inside a domain has been presented. 相似文献
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A. A. Mogul’skiĭ 《Siberian Advances in Mathematics》2013,23(4):250-262
The so-called deviation integral (functional) describes the logarithmic asymptotics of the probabilities of large deviations for random walks generated by sums of random variables or vectors. Here an important role is played by the expansion theorem for the deviation integral in which, for an arbitrary function of bounded variation, the deviation integral is represented as the sum of suitable integrals of the absolutely continuous, singular, and discrete components composing this function. The expansion theorem for the deviation integral was proved by A. A. Borovkov and the author in [9] under some simplifying assumptions. In this article, we waive these assumptions and prove the expansion theorem in the general form. 相似文献
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Xu Jiagu 《数学年刊B辑(英文版)》1984,5(2):169-184
This kind of problems is discussed:When we use certain smooth approximations of theBrownian motion W as substitutes for it in stochastic line integral and stochastic differentialequation,do these resultant integrals and solutions converge to the original one?Thecorresponding approximation theoroms for two kinds of apprximations are proved,whichare wider than those discussed in[1].Some limit theorems about stochastic line integral andsolutions of stochastic differential equations with respect to random walks are obtained byusing the idea of“embeding a random walk into the Brownian motion”first proposed byA.V.Skorohod.It seems to be remarkable that the method used here is not only effectivefor the one dimensional case,but also for the multi-dimensional case. 相似文献
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Florent Benaych-Georges 《Probability Theory and Related Fields》2009,144(3-4):471-515
We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all noncommutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically free with amalgamation over a subalgebra. Therefore, we can define a “rectangular-free convolution”, which allows to deduce the singular values of the sum of two large independent rectangular random matrices from the individual singular values. This convolution is linearized by cumulants and by an analytic integral transform, that we called the “rectangular R-transform”. 相似文献
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Zhou Xianyin 《数学年刊B辑(英文版)》1995,16(1):131-138
ONTHERANGEOFRANDOMWALKSINRANDOMENVIRONMENT¥ZHOUXIANYIN(DepartmentofMathematics,BeijingNormalUniversity,Beijing100875,China.Pr... 相似文献
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SINGULAR INTEGRAL OPERATORS ANDSINGULAR QUADRATURE OPERATORSASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS 总被引:1,自引:1,他引:0
杜金元 《数学物理学报(B辑英文版)》1998,(2)
1IntroductionSingUlarlintegralequations(SIEs)withCauchytypekernelsoftheformappearfrequelltlyinproblemsOfthetheoriesofelasticity.Heretheinputfunctionsa)b,f,l,aretheH5lder-continuousfunctionsfortheirvariables,Aisagivenconstant,anditisrequiredtofindthesolutionWintheclassho[1,2].Theclassicaltheoryoftheseequationsisrathercomplete[1,2].Inthepasttwentyyearsagreatdealofinteresthasarisenintheirnumericalsolution.VariouscollocationmethodsforSIEshaveappeared,forwhichsomereferencescanbefoundinthesurv… 相似文献
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Ding-dong Gong 《高校应用数学学报(英文版)》2008,23(3):273-278
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well. 相似文献
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By means of the definition of Hadamard principal value permutation formula and composition formula for higher order singular
integrals developing in [5], the regularization problems for higher order singular integral equations with variable coefficients
are discussed, and the higher order singular integral equations with constant coefficient are solved. It is the first time
to treat the high order singular integral equations of arbitrary degree in the theory of singular integral equations.
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In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point "environment viewed from the particle", under General Kalikow's Condition, we show the law of large numbers (LLN) and central limit theorem (CLT) for the escape speed of random walk. 相似文献
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On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Hlder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Hlder continuous property on the boundary. 相似文献
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利用积分变换技巧,作者给出了C~n中闭光滑可定向流形上一个新的Bochner-Martinelli型积分的高阶偏导数的奇异积分的Hadamard主值,获得了高阶奇异积分的Plemelj公式和合成公式,还讨论了相应的变系数线性微分积分方程的正则化,证明其可转化为一类等价的Fredholm方程。并且指出其特征方程当给出一组适当的边值条件时,在L~*中存在唯一解。 相似文献