扩散过程代数式收敛比较判敛法

研究不同的马氏半群无穷小算子之间代数式收敛的关系,获得了若干比较定理.从而可将许多一般形式的扩散算子与特殊情形进行比较,将其化归为特殊的简单易算的情形.     

R~n上扩散过程的代数式收敛

本文研究n维欧氏空间上的扩散过程在L2意义下的代数式收敛的情况,给出了判定代数式收敛的方法,并对两种特殊情形扩散算子进行了讨论.将所得判敛法应用于两个例子可得到精确的结果.     

扩散过程代数式收敛定性的判别准则

本文定性地讨论非紧空间中可逆扩散过程的代数式收敛的判定 .使用分裂空间的方法 .将全空间分裂成两个部分 :紧的子空间与非紧的余子空间 .在紧子空间中考虑边界反射的Neumann过程 ,它必然是代数式收敛的 .而在非紧子空间中考虑边界吸收的Dirichlet过程 ,如果这一Dirichlet过程以代数式的速度击中边界 ,那么就有原过程在全空间代数式收敛 ;反之 ,原过程代数式收敛 ,非紧子空间中的Dirichlet过程也是代数式收敛的 .因此过程在紧子空间的任意摄动不会影响在全空间的代数式收敛性 .     

Coexistence of algebraic and nonalgebraic limit cycles in Kukles systems

A class of Kukles differential systems of degree five having an invariant conic is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, under perturbations of the coefficients of the systems. Financed partially by: USM Grant No. 12.06.28 and 12.06.27.     

一维扩散过程的最优停止问题的研究

本文研究了一维扩散过程的最优停止问题,论证了W iener过程和几何布朗运动是F e ller过程,同时给出了一般扩散过程的处理方法.     

Iterative behaviour of generalized majority functions

Let us consider a society of n persons {P₁,…,P_n} with interaction coefficient a_ij between P_i and P_j. Let {θ₁,…,θ_p} be the set of opinions which may be assumed by any person. We study the dynamical behaviour of such a society under local majority rules.The results presented in this paper generalize many partial results previously obtained by several authors (Tchuente, 1977; Goles and Olivos, 1980; Poljak and Sura, 1982). Furthermore, by introducing algebraic invariants, analogous to those exhibited in Goles (1980) for the study of Boolean threshold functions, we provide a tool for a general approach of such dynamical models.     

Vallis系统的不变代数曲面研究

该文研究了Vallis系统的Darboux多项式和不变代数曲面问题。 在证明中,使用加权齐次多项式和特征曲线的方法,通过求解线性偏微分方程,得到了在适当的参数条件下,Vallis系统存在三类Darboux多项式。

     

The approximation of additive functionals of diffusion processes

Let us consider a diffusion process in R_d . Around each point x one may consider a ring of size ? and a process which counts the crossings over the ring. Integrating with respect to a measure μ(dx) and letting ?→ 0 one gets an additive functional. This is a natural generalization of the approximation theorem of the local time of one dimensional Brownian motion by means of “downcrossings”. For multidimensional Brownian motion the result was established by Bally. The present paper introduces a new method which allows us to handle general diffusions     

INTEGRABILITY VIA INVARIANT ALGEBRAIC CURVES FOR PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS

1 IntroductionBy definition a complex (respectively reao planar polynomial differentialsystem or simply a polynomial system is a differential system of the formdx. da.~ = i = p(x,y), ac = i = Q(x,y), (l)dt dt ~ y = Q(x,y), (l)where the dependent variables x and y are complex (respectively real), theindependent one (the time) t is real, and P and Q are polynomials in thevariables x and y with complex (respectively real) coefficients. In all thispaper m = ma-c{deg P, deg Q} denote the degree o…     

Classification of bernstein algebras of type (3, n - 3)

A classification of Bernstein algebras in dimensions n ? 4 has been made by Holgate in [2], however that article contains no classification up to isomorphism, the problem is solved by Lyubich in [4] when K = R or C, and by Cortes [1] in the general case. Also Lyubich has given in [5] a classification of the regular nonexceptional Bernstein algebra of type (3,n?3) and a classification but not up to isomorphism of nonregular nonexceptional Bernstein algebras of type (3,n ? 3) when K = C. The aim of this paper it to characterize, up to isomorphism, Bernstein algebras of type(2, n ? 2) and nonexceptional of type(3, n ?3) over a infinite commutative field K whose characteristic is different from 2.     

Stochastic differential inclusions and diffusion processes

Connections between weak solutions of stochastic differential inclusions and solutions of partial differential inclusions, generated by given set-valued mappings are considered. The main results are based on some continuous approximation selection theorem and weak compactness of the set of all weak solutions to a given stochastic differential inclusion.     

General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group Cr(P k n ) of Birational Transformations

A general approach is developed for integrating an invertible dynamical system defined by the composition of two involutions, i.e., a nonlinear one which is a standard Cremona transformation, and a linear one. By the Noether theorem, the integration of these systems is the foundation for integrating a broad class of Cremona dynamical systems. We obtain a functional equation for invariant homogeneous polynomials and sufficient conditions for the algebraic integrability of the systems under consideration. It is proved that Siegel's linearization theorem is applicable if the eigenvalues of the map at a fixed point are algebraic numbers.