Symmetry in non-linear stochastic dynamical systems and its applications

非线性随机动力系统的对称性及其应用

基本信息

  • 批准号:
    08640300
  • 负责人:
  • 金额:
    $ 0.7万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    1995
  • 资助国家:
    日本
  • 起止时间:
    1995 至 1996
  • 项目状态:
    已结题

项目摘要

The present study focuses on the theory of symmetry for stochastic non-linear dynamical systems described by stochastic differential equations. Here symmetry means an one-parameter continuous transformation which leaves the stochastic system invariant. Within the framework, the following results are obtained.1) A method for deriving conserved quantities from symmetry is developed, and thereby the new conserved quantities are obtained for the non-linear stochastic systems.2) The similarity method is formulated to stochastic systems ; that is, if a stochastic dynamical system admits symmetry, it follows that the order of stochastic equations describing the system can be reduced. It is examined that the method is useful to analyze stochastic non-linear systems.As the related topics, numerical simulations of a stochastic Kaldor business cycle model, which is a typical example of stochastic non-linear system, and stochastic analysis of the pricing problem of contingent claims are treated.In the first topic, the numerical results indicate that noise in the model may not only obscure the underlying dynamical structures, but also reveal the hidden structures, for example, the chaotic attractors near a window of chaos or the periodic attractors near a small chaotic parameter region.In the second topic, an equivalent martingale mesure for the probability measure assigned to the price process of stocks, which may be regarded as a genaral stodhastic dynamical system, plays an important role to determine the price of contingent claims. If the market is incomplete, there are many equivalent martingale measures. Hence the minimization principle of relative entropy is adopted for a criterion of reasonable martingale measure ; the obtained measure is called the canonical martingale measure (CMM). The existence of CMM and the relations between CMM and the minimal martingale measure are investgated.
本文主要研究用随机微分方程描述的随机非线性动力系统的对称性理论。这里对称是指使随机系统保持不变的单参数连续变换。在该框架内,得到了以下结果。1)提出了一种由对称性推导守恒量的方法,从而得到了非线性随机系统的新守恒量。2)将相似方法应用于随机系统;也就是说,如果一个随机动力系统允许对称,那么描述该系统的随机方程的阶数可以降低。验证了该方法对随机非线性系统的分析是有用的。本文对随机非线性系统的典型例子——随机卡尔多经济周期模型进行了数值模拟,并对或有债权定价问题进行了随机分析。在第一个主题中,数值结果表明,模型中的噪声不仅会掩盖潜在的动力学结构,而且会揭示隐藏的结构,例如混沌窗口附近的混沌吸引子或小混沌参数区域附近的周期吸引子。在第二个主题中,分配给股票价格过程的概率测度的等效鞅测度可以看作是一个一般的随机动力系统,它在确定或有债权的价格方面起着重要的作用。如果市场是不完全的,则有许多等效的鞅度量。因此,采用相对熵最小化原理作为合理鞅测度的判据;得到的测度称为正则鞅测度(CMM)。研究了CMM的存在性以及CMM与最小鞅测度的关系。

项目成果

期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A. Dohtani: "Chaos, complex transients and noise : illustration with Kaldor model" Chaos Solitons & Fractals. 7・12. 2157-2174 (1996)
A. Dohtani:“混沌、复杂瞬态和噪声:卡尔多模型的插图”混沌孤子和分形 7・12 (1996)。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
Y.Miyahara: "Canonical martingale measures and minimal martingale measures of incomplete assets markets" The Australian National Univ.Research Report. vol.007-96. 95-100 (1996)
Y.Miyahara:“不完全资产市场的规范鞅措施和最小鞅措施”澳大利亚国立大学研究报告。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
T.Misawa: "Conserved quantities and symmetries in stochastic dynamical systems" Inst.of Statist.Math., Cooperative Research Report (in Japanese). vol.91. 79-88 (1996)
T.Misawa:“随机动力系统中的守恒量和对称性”Inst.of Statist.Math.,合作研究报告(日语)。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

MISAWA Tetsuya其他文献

MISAWA Tetsuya的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('MISAWA Tetsuya', 18)}}的其他基金

Dynamical Risk Sensitive Value Measure and its Application to Valuation of Project
动态风险敏感价值测度及其在项目评估中的应用
  • 批准号:
    18K03421
  • 财政年份:
    2018
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Risk analysis for the evaluation of investment in the framework of stochastic dynamical theory
随机动力学理论框架下投资评估的风险分析
  • 批准号:
    24540136
  • 财政年份:
    2012
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Risk analysis based on stochastic dynamical systems theory
基于随机动力系统理论的风险分析
  • 批准号:
    21540140
  • 财政年份:
    2009
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Symmetry on stochastic discrete dynamical systems and the related topics
随机离散动力系统的对称性及相关主题
  • 批准号:
    18540134
  • 财政年份:
    2006
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Lie algebra & group methods to non-linear stochastic dynamical systems and its applications
李代数
  • 批准号:
    14540133
  • 财政年份:
    2002
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Conserved quantities and symmetries in non-linear stochastic dynamical systems and its applications
非线性随机动力系统中的守恒量和对称性及其应用
  • 批准号:
    11640132
  • 财政年份:
    1999
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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
  • 批准号:
    09640285
  • 财政年份:
    1997
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

相似海外基金

Structure-Preserving Integrators for Lévy-Driven Stochastic Systems
Levy 驱动随机系统的结构保持积分器
  • 批准号:
    EP/Y033248/1
  • 财政年份:
    2024
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Research Grant
CAREER: Identifying emergent dynamics in stochastic systems
职业:识别随机系统中的新兴动态
  • 批准号:
    2238667
  • 财政年份:
    2023
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Continuing Grant
Rare Events and High-Dimensional Stochastic Systems
稀有事件和高维随机系统
  • 批准号:
    2246838
  • 财政年份:
    2023
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Standard Grant
Learning Complex Stochastic Systems
学习复杂的随机系统
  • 批准号:
    2246815
  • 财政年份:
    2023
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Standard Grant
Construction and systematization of unified control theory for discrete-time stochastic systems
离散时间随机系统统一控制理论的构建和系统化
  • 批准号:
    23H01433
  • 财政年份:
    2023
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Multi-scale stochastic systems motivated by biological models
由生物模型驱动的多尺度随机系统
  • 批准号:
    RGPIN-2015-06573
  • 财政年份:
    2022
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Discovery Grants Program - Individual
Optimising stochastic systems using streaming simulation.
使用流模拟优化随机系统。
  • 批准号:
    2753514
  • 财政年份:
    2022
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Studentship
Dynamical Approaches for Some Complex Stochastic Systems
一些复杂随机系统的动力学方法
  • 批准号:
    2205972
  • 财政年份:
    2022
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Standard Grant
New universality in stochastic systems
随机系统的新普遍性
  • 批准号:
    DP220100973
  • 财政年份:
    2022
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Discovery Projects
Modeling, Analysis, Optimization, Computation, and Applications of Stochastic Systems
随机系统的建模、分析、优化、计算和应用
  • 批准号:
    2204240
  • 财政年份:
    2022
  • 资助金额:
    $ 0.7万
  • 项目类别:
    Continuing Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了