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991.
倒向随机微分方程由Pardoux和彭实戈首先提出,彭实戈给出了一维BSDE的比较定理,周海滨将其推广到了高维情形.毛学荣将倒向随机微分方程解的存在唯一性定理推广到非Lipschitz系数情况,曹志刚和严加安给了相应的一维比较定理.本文将曹志刚和严加安的比较定理推广到高维情形. 相似文献
992.
In this paper, we extend the Hölderian invariance principle of Lamperti [6] to the case of partial-sum processes based on a triangular array of row-wise independent random variables. As an application, we obtain necessary and sufficient conditions for the almost sure (resp. in probability) weak Hölder convergence of partial-sum processes based on bootstrapped samples. 相似文献
993.
时间随机环境下随机游动的渐近行为 总被引:2,自引:0,他引:2
本文给出了可数状态空间中时间随机环境下随机游动的一个统一的模型 .对于最常见的情况 ,即d维最近邻域随机环境下随机游动 ,如果环境是严平稳的 ,则在一定条件下 ,该随机游动满足强大数定律和中心极限定理 .特别地 ,当环境独立同分布时 ,我们可以得到更为具体的结果 ,该结果类似于经典的随机游动的相应结论 . 相似文献
994.
We obtain a central limit theorem for a general class of additive parameters (costs, observables) associated to three standard Euclidean algorithms, with optimal speed of convergence. We also provide very precise asymptotic estimates and error terms for the mean and variance of such parameters. For costs that are lattice (including the number of steps), we go further and establish a local limit theorem, with optimal speed of convergence. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various other techniques: Dirichlet series, Perron's formula, quasi-powers theorems, and the saddle-point method. Such dynamical analyses had previously been used to perform the average-case analysis of algorithms. For the present (dynamical) analysis in distribution, we require estimates on transfer operators when a parameter varies along vertical lines in the complex plane. To prove them, we adapt techniques introduced recently by Dolgopyat in the context of continuous-time dynamics (Ann. Math. 147 (1998) 357). 相似文献
995.
Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2006,323(1):267-274
Using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for T for which the a-Browder's theorem or the a-Weyl's theorem holds. Also, the relation between hypercyclic operators (or supercyclic operators) and the operators which satisfy Weyl type theorem is discussed. 相似文献
996.
A. Dzhumadil’daev 《Siberian Mathematical Journal》2006,47(4):643-652
We prove that an associative commutative algebra U with derivations D 1, ..., D n ε DerU is an n-Lie algebra with respect to the n-multiplication D 1 ^ ? ^ D n if the system {D 1, ..., D n } is in involution. In the case of pairwise commuting derivations this fact was established by V. T. Filippov. One more formulation of the Frobenius condition for complete integrability is obtained in terms of n-Lie multiplications. A differential system {D 1, ..., D n } of rank n on a manifold M m is in involution if and only if the space of smooth functions on M is an n-Lie algebra with respect to the Jacobian Det(D i u j ). 相似文献
997.
Marc Chamberland 《Journal of Number Theory》2006,120(2):349-371
We study congruence and divisibility properties of a class of combinatorial sums that involve products of powers of two binomial coefficients, and show that there is a close relationship between these sums and the theorem of Wolstenholme. We also establish congruences involving Bernoulli numbers, and finally we prove that under certain conditions the sums are divisible by all primes in specific intervals. 相似文献
998.
S. V. Shaposhnikov 《Mathematical Notes》2006,79(3-4):413-430
We give a complete proof of Morrey’s estimate for the W 1,p -norm of a solution of a second-order elliptic equation on a domain in terms of the L 1-norm of this solution. The dependence of the constant in this estimate on the coefficients of the equation is investigated. 相似文献
999.
Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker
in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to
be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the
flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically,
can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As
a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen
theorem proved in the context of the random walker's maximum. 相似文献
1000.
The main aim of this paper is to improve some results obtained by Mao [X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Nonlinear Stud. 7 (2000) 307-328]. Our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above. For example, we need only the local Lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions. To guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation (SFDE) under the weaker conditions imposed in this paper, we establish a generalised existence-and-uniqueness theorem which covers a wider class of nonlinear SFDEs as demonstrated by the examples discussed in this paper. Moreover, from our improved results follow some new criteria on the stochastic asymptotic stability for SFDEs. 相似文献