Ergodic BSDEs under weak dissipative assumptions

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying forward equation, which, on the contrary, is assumed to be non-degenerate.We show the existence of solutions by the use of coupling estimates for a non-degenerate forward stochastic differential equation with bounded measurable nonlinearity. Moreover we prove the uniqueness of “Markovian” solutions by exploiting the recurrence of the same class of forward equations.Applications are then given for the optimal ergodic control of stochastic partial differential equations and to the associated ergodic Hamilton-Jacobi-Bellman equations.     

An overshoot approach to recurrence and transience of Markov processes

We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between +∞ and −∞. The conditions are based on a Markov chain which only consists of jumps (overshoots) of the process into complementary parts of the state space.In particular, we show that a stable-like process with generator −(−Δ)^α(x)/2 such that α(x)=α for x<−R and α(x)=β for x>R for some R>0 and α,β∈(0,2) is transient if and only if α+β<2, otherwise it is recurrent.As a special case, this yields a new proof for the recurrence, point recurrence and transience of symmetric α-stable processes.     

求m阶递推数列通项公式的两种方法

利用分析中的解析函数方法和代数中的矩阵方法,得到了m阶常系数齐次线性递推数列通项公式的解析表达式,是对已有结果的完善和推广.     

Recurrence propagation equation of Hermite-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples.     

Some Indeterminate Moment Problems and Freud-Like Weights

We study two indeterminate Hamburger moment problems and the corresponding orthogonal polynomials. The coefficients in their recurrence relations are of exponential growth or are polynomials of degree 2. The entire functions in the Nevanlinna parametrization are found. The orthogonal polynomials with polynomial recurrence coefficients resemble the Freud polynomials with a = 1/2 . Inequalities are given for the largest zero and the asymptotic behavior of the largest zero is established. April 24, 1996. Date revised: March 3, 1997.     

电场中Rydberg原子的常数标度能谱方法

标度能谱理论能够简化外场谱及可以经典方法理解原子外场谱而倍受关注。本文报道了用于电场中Rydberg原子常数标度能谱实验研究的装置以及有关的计算机控制、采集及处理系统。该系统对能量E和电场F进行同步控制以保持标度能谱ε=E/F为常数，并成功地得到Rydberg态Sr原子在标度能ε=-3.0时的标度能谱，经过傅里叶变换，获得了电场中Sr原子的电子回归谱。     

一类E-Vandermonde矩阵的求逆及逆的迭代公式

本文给出一类E-Vandermonde矩阵和广义E-Vandermonde矩阵可逆的条件及逆的矩阵表达式，并给出了求逆的迭代公式．     

Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces

The aim of this paper is to establish the semilocal convergence of a multipoint third order Newton-like method for solving F(x)=0 in Banach spaces by using recurrence relations. The convergence of this method is studied under the assumption that the second Fréchet derivative of F satisfies Hölder continuity condition. This continuity condition is milder than the usual Lipschitz continuity condition. A new family of recurrence relations are defined based on the two new constants which depend on the operator F. These recurrence relations give a priori error bounds for the method. Two numerical examples are worked out to demonstrate the applicability of the method in cases where the Lipschitz continuity condition over second derivative of F fails but Hölder continuity condition holds.     

Modelling the Recurrence of Bladder Cancer

The risk of a new tumor recurrence after transurethral resection (surgical operation) in patients with primary superficial bladder carcinoma is evaluated. As the exact time of the event is not known, it is suggested to consider interval-censored survival data methodology. We use the model of Farrington to perform a prognostic model for predicting a new recurrence and to determine the clinicopathologic factors associated within interval-censored data framework. The implementation of this method is easy using standard statistical packages. Anyway, we use diagnostic methods for the validation of the model developed by the same author for interval-censored data. The obtained model is easily interpretable and let us to individualize the course of follow-up and treatment of each patient in order to improve the patient’s quality of life.      

A REMARK ON EXTINCTION OF A CLASS OF SUPERPROCESSES

1.IntroductionSuperprocesses,i.e.,measure-vauedMarkovprocesses,havebeenanattractivetopicintherecenty6ars,whichcanbedefinedasfollows.Let((,Px)..MbeaMarkovprocesswithstrongcontinuousMarkovsemigroupSt(denotebyAitsinfinitesimaloperator,andbyPt(x,y)theassociatedtransitiollfunction).DenotebyMPthesetofallRadonmeasurespsatisfyingandbypC(t)(resp.pCc(t))thesetofpositivelycontinuousfUnctions(resp.withcompactsupport)int-Thesthcalledsuperprocess(X,P#).6MPwithparameters(andopandtakingvalueinMrisdete…