两参数广义Poisson过程

定义了两参数广义Ｐｏｉｓｓｏｎ过程，得到了它的基本性质、局部鞅性和各种两参数Ｍａｒｋｏｖ性，研究了它的跳线和样本函数，对跳线和样本函数作了形象、明确和深刻的刻划，可以说是一目了然的。     

索赔到达过程为马氏跳过程的一类风险模型

论将索赔到达点过程由Poisson点过程推广为由马氏链的跳跃点形成的点过程，保费收取由净收入随机确定，我们得到破产概率ψ（u)及条件破产概率φi(u)满足的积分方程．     

Delphic-半群与随机点过程

本文把D.G.Kendall提出的Delphic-半群理论应用于随机点过程,首先证明了在完备可分距离空间上任一随机点过程的因子全体为紧集这一基本引理,进而证明了某些随机点过程族构成的半群在适当定义同态变换后为Delphic-半群。例如有限点过程族的卷积半群,如取点过程的特征母泛函的负对数为所要求的同态变换构成Delphic-半群。     

以分数布朗运动为输入过程的存储过程生成的上穿点过程

本文研究了以分数布朗运动为输入过程的存储过程上穿高水平u形成的点过程的渐近泊松特性,结果表明当分数布朗运动参数H∈(0,1/2),u→∞时,该点过程弱收敛到泊松过程.     

两个相关更新过程的一种新描述

研究了两个相关点过程之间相关性的描述。我们指出当两个点过程是泊淞过程时，相关系数能充分描述它们之间的相互关系。当两个点过程是更新过程时，相关系数随着时间窗口的变化而变化，是时间窗口的递增函数。于是我们提出用相关系数曲线来描述两个更新过程之间的相互关系。这些结论对优化神经网络的设计将是很有用的。     

点到集映像和点到集映像族的连续化

一个最优化算法的迭代过程,可以看做一个点到集映像的取值过程。从这个观念出发,Zangwill建立了全局收敛定理,统一了许多算法的收敛性证明。但是,同一个算法可以看做许多不同的点到集映像的取值过程。事实上,把一点对应于从该点按算法可能达到的下一点的全体形成的点到集映像称为算法所对应的点到集映像,那么,任一点到集映像,若它的像集于任一点外都包含算法所对应的点到集映像的像集,其取值过程均包含了     

以分数布朗运动为输入过程的存储过程生成的上穿点过程（英文）

本文研究了以分数布朗运动为输入过程的存储过程上穿高水平u形成的点过程的渐近泊松特性,结果表明当分数布朗运动参数H∈(0,1/2),u→∞时,该点过程弱收敛到泊松过程.     

关于Q过程跳跃次数的一个注记

本文考虑一类Ｑ过程的跳次数及相应的点过程，证明了与此点过程有关的一个随机积分是平方可积鞅，同时对有关文献中的不足之处作了讨论。     

构造方程模型解几何中动点问题

几何中动点问题的特点是:图形中的动点或动线按某种规律运动,各个动点或动线在运动变化的过程中互相依存,要探求动点或动线运动到何位置时满足一定的"图形条件".……     

一类Gauss序列极值的极限律

本文讨论一类非平稳Gauss序列的极值．利用点过程收敛定理得到多水平超过的点过程的收敛性,同时得到在不相交区间上最大值的联合渐近分布,第k个最大值的渐近分布以及前r个极值的联合渐近状态．     

Point processes in the plane

In this survey paper, two-parameter point processes are studied in connection with martingale theory and with respect to the partial-order induced by the Cartesian coordinates of the plane. Point processes are characterized by jump stopping times and by their two-parameter compensators. Properties of the doubly stochastic Poisson process, such as predictability, are discussed. A definition for the Palm measure of a two-parameter stationary point process is proposed.     

Two-parameter diffusion processes and martingales

We introduce a class of two-parameter processes which are diffusions on each coordinate and satisfy a particular Markov property related to the partial ordering in R²₊. These processes can be expressed as solutions of some stochastic integral equations driven by a two-parameter Wiener process and two families of ordinary Brownian motions. This result is based on a characterization of two-parameter martingales with orthogonal increments.     

Two-Parameter Fuzzy-Valued Stochastic Integrals and Equations

This article is concerned with notions of fuzzy-valued stochastic integrals driven by two-parameter martingales and increasing processes. We present their main properties and formulate next two-parameter fuzzy-valued stochastic integral equations. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.     

A diffusion approximation result for two parameter processes

Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010     

Two parameter optimal stopping and bi-Markov processes

Summary In this paper, the optimal stopping problem is solved for particular two-parameter processes, here called bi-Markov processes. A subsequent potential theory is developed with respect to a pair of one-parameter semi-groups. We introduce a new notion of harmonicity for two-variable functions and we interpret it in the framework of the theory of bi-Markov processes.     

Double $S$-Breaking Cubic Turning Points and Their Computation

1.Introducti0nManynaturalphen0menapossessm0reorlessexactsymmetries,whicharelikelytobereflectedinanysensiblemathematicalm0del.Idealizationssuchasperiodicboundaryconditi0nscanproduceadditionaJsymmetries.Phen0menawhosemodelsexhibitbothsymmetryandnonlinearityleadtopr0blemswhicharechallengingandrichinc0mplexity.Problemswithsymmetriescanshowarichbifurcationbehavi0ur.Theoccurrenceofmultiplesteadystatebifurcationismostlyduetounderlyingsymmetries.Thisgivesrisetothedifficultiestonumericalcomputation-H…     

Hölder Exponent for a Two-Parameter Lévy Process

We study the regularity of a two-parameter Lévy process in the neighbourhood of a fixed point and then we compute the Hölder exponent of such a process.     

Set-Valued Stochastic Integrals and Equations with Respect to Two-Parameter Martingales

This article is concerned with notions of set-valued stochastic integrals driven by two-parameter martingales and increasing processes. We investigate their main properties and we consider next multivalued stochastic integral equations in the plane. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.     

Fubini theorem for multiparameter stable process

We prove stochastic Fubini theorem for general stable measure which will be used to develop some identities in law for functionals of one and two-parameter stable processes. This result is subsequently used to establish the integration by parts formula for stable sheet.     

Snap-through buckling of a shallow arch resting on a two-parameter elastic foundation

In this paper, we study the static and dynamic snap-through of a shallow arch resting on a two-parameter elastic foundation under a point load moving at a constant speed. The deformation of the arch is expressed in Fourier series. We extend the previous works when the arch resting on a certain model of two-parameter elastic foundation. Each model of foundation has a different definition for the second foundation parameter, where the model is discussed in this paper is Pasternak model. For quasi-static analysis, it is noted that the first four modes in the expansion are sufficient to predict the response of the arch. Similarly, when the point load moves with a significant speed, we integrate the equation of motion numerically using the first modes in the expansion.