Bifurcations and Dynamics of Spiral Waves

(N) . In this article, it is shown that the dynamics near meandering spiral waves or other patterns is determined by a finite-dimensional vector field that has a certain skew-product structure over the group SESE(N) . This generalizes our earlier work on center-manifold theory near rigidly rotating spiral waves to meandering spirals. In particular, for meandering spirals, it is much more sophisticated to extract the aforementioned skew-product structure since spatio-temporal rather than only spatial symmetries have to be accounted for. Another difficulty is that the action of the Euclidean symmetry group on the underlying function space is not differentiable, and in fact may be discontinuous. Using this center-manifold reduction, Hopf bifurcations and periodic forcing of spiral waves are then investigated. The results explain the transitions to patterns with two or more temporal frequencies that have been observed in various experiments and numerical simulations. Received December 8, 1997; accepted May 19, 1996     

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.     

Stochastic Fubini Theorem for Jump Noises in Banach Spaces

We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.     

加性二值噪声激励下Duffing系统的随机分岔

研究了Duffing系统在加性二值噪声作用下的随机分岔现象.首先,根据二值噪声的统计特性,推导得到二值噪声状态间的跃迁概率,据此对二值噪声进行了数值模拟.其次,利用四阶Runge-Kutta(龙格-库塔)数值算法得到该系统位移和速率的稳态联合概率密度及位移的稳态概率密度.然后,通过对位移稳态概率密度单双峰结构变化的研究,发现加性二值噪声的状态和强度能够诱导系统产生随机分岔现象.最后,观察到随着系统非对称参数的逐渐变化,系统同样产生了随机分岔现象.     

A General Benchmark Model for Stochastic Jump Sizes

Abstract

Under few technical assumptions and allowing for the absence of an equivalent martingale measure, we show how to price and hedge in a sequence of incomplete markets driven by Wiener noise and a marked point process. We investigate the structure of market prices of risk as markets become approximately complete and consider the limits of traded securities, characterizing explicitly the growth optimal portfolio and investigating arbitrage and diversification in such markets.     

马尔可夫跳跃双线性离散随机系统的稳定性

本研究了一类带有马尔可夫姚跃参数的双线性离散随机系统的稳定性，获得了该系统的稳定性和能稳定性的充分条件。     

跳过程随机可比的充要条件

本文研究跳过程的随机可比性·基于文献［２］和［３］,证明两个跳过程随机可比的充要条件是其ｑ对可比·同时,改进了［６］中唯一性问题的结果     

Sufficient and Necessary Conditions for Stochastic Comparability of Jump Processes

Abstract This note is devoted to the study of the stochastic comparability of jump processes. On the basis of [2] and [3], it is proved that two jump processes are stochatically comparable if and only if their q-pairs are comparable. Meanwhile, the result concerning the uniqueness given in [6] is also improved upon. Research supported in part by DPFIHE(Grant No.96002704), NNSFC(Grant No.19771008), MCSEC, Ying-Tung Fok Educational Foundation and Youth Science Foundation of BNU     

Dynamics Aggregation in Stochastic Control Problems

For stochastic control problems with mixed state-control constraints, we develop a dynamics aggregation method which replaces the stochastic differential or difference equation with a simpler constraint. Solutions of such simplified problems are used to construct a sequence of approximations to the original problem. Convergence properties of the method for both discrete-time and continuous-time models are analyzed in detail.     

On Dynamic Aspects and Pattern Generation in Vehicle-Road Interaction

Increasing transport capacity leads to new vehicle designs and increasing axle loads. Still it has to be better understood until which extend especially heavy vehicles cause corrugation of roads. Therefore, basic investigations concerning vehicle-road interaction are helpful to augment the understanding of the basic mechanisms. Firstly, in order to investigate the oscillatory behavior of a vehicle a MDoF oscillator moving with constant velocity on a rippled road is considered. From this, general results about wear pattern generation of the road are derived from analytical considerations concerning the dynamic contact force between vehicle and road. Secondly, a simple vehicle road interaction model is presented which consists of a vehicle model and a road exhibiting viscoelastic plastic characteristics. Results of numerical simulations are compared with the findings deduced from the analytical MDoF model. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Backward Stochastic Differential Equations for a Single Jump Process

We consider backward stochastic differential equations (BSDEs) related to a finite continuous time single jump process. We prove the existence and uniqueness of solutions when the coefficients satisfy Lipschitz continuity conditions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated.     

Backward Stochastic Difference Equations for a Single Jump Process

We define Backward Stochastic Difference Equations related to a discrete finite time single jump process. We prove the existence and uniqueness of solutions under some assumptions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated. In this paper the single jump process takes values in a general measurable space where as previous work has considered the situation where the noise is a finite state Markov chain, so the state space is finite.     

Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment

This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters. Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.     

非对称碰撞约束下形状记忆合金梁的随机响应与分岔

形状记忆合金(SMA)是二十一世纪具有形状记忆效应的新型智能材料.针对具有非对称约束的SMA梁,本文构造了碰撞振动系统.在无碰撞和有碰撞两种情况下,利用随机平均法给出了近似解析结果.数值模拟作为验证解析结果的工具.结果表明,系统能量的概率响应曲线具有非光滑特性.当约束位置发生变化时,系统会出现随机P分岔和D分岔.     

国际油价波动跳跃性特征的实证分析

根据国际油价波动中存在异常跳跃的情况,本文运用EGARCH-Jump模型对国际油价波动的跳跃性特征进行了实证分析。结果表明,加入跳跃因素的模型减缓了国际油价波动的持续性,同时杠杆效应消失,表明跳跃性因素是国际油价波动的影响因素之一,也证实了国际油价波动的跳跃性特征是国际石油市场产生杠杆效应的原因。但从长期来看,跳跃性因素对国际油价波动的扰动影响并不大,国际油价的波动仍主要受正常信息的影响。总体上,EGARCH-Jump模型比普通GARCH族模型能更好地捕捉国际油价波动的动态性特征。     

跳扩散模型下的非零和随机微分投资组合博弈

现实经济中,当股票价格受到一些重大信息影响而发生突发性的跳跃时,用跳扩散过程来描述股票价格的趋势更符合实际情况。基于这一观察,本文研究跳扩散模型下包含两个投资者的非零和投资组合博弈问题。假设金融市场中包含一种无风险资产和一种风险资产,其中风险资产的价格动态用跳扩散模型来描述。将该非零和博弈问题构造成两个效用最大化问题,每个投资者的目标是最大化终端时刻自身财富与其竞争对手财富差的均值-方差效用。运用随机控制理论,得到了均衡投资策略以及相应值函数的解析表达。最后通过数值仿真算例分析了模型相关参数变动对均衡投资策略的影响。仿真结果显示:当股价发生不连续跳跃,投资者在构造投资策略时考虑跳跃风险可以显著增加其效用水平;同时,随着博弈竞争的加剧,投资者为了在竞争中取得更好的表现,往往会采取更加激进的投资策略,增加对风险资产的投资。     

Jump Lq-Optimal Control For Discrete-Time Markovian Systems With Stochastic Inputs

In this paper we consider the discrete-time LQ-optimal control problem for the class of linear systems with Markovian jump parameters and additive l ₂-stochastic input. The state-space of the Markov chain is assumed to be a countably infinite set. The controller has access to both the state-variable and jump-variable. It is shown that the optimal control law is characterized by a feedback term plus a term defined by the:l ₂-stochastic input and Markov chain. An application to the optimal control of a failure prone manufacturing system subject to a random demand for a single type of item is presented.     

Necessary Maximum Principle of Stochastic Optimal Control with Delay and Jump Diffusion

In this paper, we have studied the necessary maximum principle of stochastic optimal control problem with delay and jump diffusion.     

基于带跳随机波动率模型的双币种重置期权定价研究

研究了外国标的资产价格,汇率及其波动率过程满足仿射跳扩散模型的双币种重置期权定价问题,其中波动率过程与标的资产,汇率相关,且具有共同跳跃风险成分.利用多维Feynman-Kac定理,Fourier逆变换等方法,获得了双币种重置期权价格的表达式.应用数值计算分析了波动率过程主要参数对期权价格的影响.数值结果表明,波动率因素以及跳跃风险参数对期权价格的影响是显著的.