Limiting laws for long Brownian bridges perturbed by their one-sided maximum, III

Summary Results of penalization of a one-dimensional Brownian motion ]]>]]>]]>]]>]]>]]>]]>(X_t) $, by its one-sided maximum $\big(S_t=\sup_{0 \leq u \leq t}X_u\big)$, which were recently obtained by the authors are improved with the consideration - in the present paper - of the asymptotic behaviour of the likewise penalized Brownian bridges of length $t$, as $t\rightarrow \infty$, or penalizations by functions of $(S_t,X_t)$, and also the study of the speed of convergence, as $t\rightarrow \infty$, of the penalized distributions at time $t$.     

条件Erlang分布的双参数加法定理

X(γ)和Y(k)服从参数(γ,λ)和(k,μ)的Erlang分布且相互独立.本文证明了在X(γ)相似文献   

A novel cryptosystem based on grey system theory and genetic algorithm

In this paper, we first attempt to introduce the biological concepts of genetic factor and genetic variation into the study of a Kaleidoscope–Queer (in brief, K–Q) cryptosystem. The novel K–Q cryptosystem including the genetic factor, (GM, X, λ(x)), can be applied to ensure the security of an information system. The main contributions include the K–Q cryptosystem concept with genetic factor, the existence theorem of -era K–Q cryptosystem with genetic factor, the limited embedded theorem of K–Q cryptosystem with genetic factor, and the genetic variability theorem of K–Q cryptosystem.     

ON THE EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR SINGULAR p-LAPLACE EQUATIONS

In this paper N-dimensional singular, p-Laplace equations of the following form are considered, where p ≥N, β > 0, and f : [0,∞)×(0,∞)×[0, ∞)→[0,∞) is a continuous function. Some sufficient conditions are obtained for the existence of infinitely many radially positive entire solutions of the equation which are asymptotic to positive constant multiples of |x|(p-N)/(p-1) for p > N or log|x| for N = p as |x|→∞.     

Time shifted aliasing error upper bounds for truncated sampling cardinal series

Time shifted aliasing error upper bound extremals for the sampling reconstruction procedure are fully characterized. Sharp upper bounds are found on the aliasing error of truncated cardinal series and the corresponding extremals are described for entire functions from certain specific Lp, p>1, classes. Analogous results are obtained in multidimensional regular sampling. Truncation error analysis is provided in all cases considered. Moreover, sharpness of bounding inequalities, convergence rates and various sufficient conditions are discussed.     

Relative Compactness for Capacities, Measures, Upper Semicontinuous Functions and Closed Sets

We prove an Ascoli theorem for capacities. This theorem which characterizes relatively compact sets of capacities is widely applicable and many Ascoli theorems for particular classes of capacities can immediately be deduced as corollaries. Indeed it is usually necessary only to demonstrate that these classes are closed and then to simplify the characterization when possible. In particular, we show that the proof of the classical Prohorov theorem can be naturally factored into the shorter proof of the Ascoli theorem for capacities and into the somewhat longer proof that the class of probability measures is closed in the class of capacities. We also deduce new and known Ascoli theorems for sup measures, upper semi-continuous functions, the Vietoris hyperspace topology, and various classes of measures.     

拟线性滞后型微分方程正解的存在性

本文研究了下面这种拟线性滞后型微分方程(g(u′)′+a(t) f (ut) =0 ,　　 0 1 ,满足非线性边界条件 .并且通过应用锥不动定理与阿尔采拉 -阿斯卡里定理 ,证明了上述方程至少存在一个正解 .     

Free energy and some sample path properties of a random walk with random potential

We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.     

Cauchy微分中值定理的推广的一个简单证明

给出Cauchy微分中值定理的推广的一个简单证明.     

On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria

In this paper we study the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences, under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given σ-algebra, as done in Gordin (Dokl. Akad. Nauk SSSR 188, 739–741, 1969) and Heyde (Z. Wahrsch. verw. Gebiete 30, 315–320, 1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations or regular functions of linear processes.