Stochastic numerical schemes to stochastic dynamical systems with conserved quantities

具有守恒量的随机动力系统的随机数值格式

基本信息

批准号：
09640285
负责人：
MISAWA Tetsuya
金额：
$ 0.45万
依托单位：
Nagoya City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

This study is dealt with the stochastic difference schemes and related topics for stochastic dynamical systems governed by stochastic differential equations which have conserved quantities. The head investigator, T.Misawa, focuses on an one-dimensional stochastic Hamilton dynamical system in which the energy function (Hamiltonian) becomes a conserved quantity. For the system, he proposes two energy conservative stochastic difference schemes which leave Hamiltonians numerically invariant. and proves that the local error orders of accuracy of numerical solutions derived from the stochastic schemes are 2 and 4 respectively. Moreover, as a fundamental study for the thema, Nisawa also investigates on a method for deriving conserved quantities from symmetry in stochastic systems, the similarity method (a method of the reduction of the order of stochastic equations), and the relations between conserved quantities and symmetry in stochastic Hamilton systems.As the related topics, Misawa treats the numerical simulations of a stochastic business cycle model in an open economy, a wavelet interpolation method with simulated annealing in time series analysis. A.Shimizu works with a genealogical problem of a stepping stone Fleming-Viot process and examines the fractional moments of the first returning time of positively recurrent Markov.chains. Y.Miyahara is concerned with stochastic analysisof the pricing problem of contingent claims ; he investigates on minimal entropy martingale measures of jump type price processes in incomplete assets markets. Y.Hashimoto deals with in the relation between positive-definite generalized functions and the heat kernel. Through the studies, we find out that stochastic numerical method is useful for the analysis of the several stochastic problems in such topics.

这项研究涉及由具有保守量的随机微分方程控制的随机动力学系统的随机差异方案和相关主题。首席研究员T.Misawa专注于一维随机汉密尔顿动力系统，其中能量功能（汉密尔顿）成为保守数量。对于该系统，他提出了两个能源保守的随机差异方案，这些计划使汉密尔顿人数值不变。并证明从随机方案得出的数值解的局部误差顺序分别为2和4。此外，作为对thea的基础研究，Nisawa还研究了一种在随机系统中从对称性中得出保守数量的方法时间序列分析中使用模拟退火的插值方法。 A.shimizu处理了垫脚石弗莱明 - 维奥特过程的族谱问题，并研究了正式经常性马可福音的第一个返回时间的分数时刻。 Y.Miyahara关注定价问题的随机分析；他调查了不完整资产市场中跳高型价格过程的最小熵措施。 Y.Hashimoto在正定普通函数与热核之间的关系中处理。通过研究，我们发现随机数值方法可用于分析此类主题中的几个随机问题。