Longterm behaviour of interacting stochastic (partial) differential equations and combinatorial stochastic processes, with a focus on the method of duality

相互作用的随机(偏)微分方程和组合随机过程的长期行为,重点是对偶方法

基本信息

项目摘要

The method of duality is a mathematical formalism that allows to find close connections between certain properties, such as moments or the long-term behaviour, of two not necessarily related stochastic processes. Often it is possible to study important properties of a complicated stochastic process, e.g. described by a stochastic partical differential equation, by analysing the properties of a simpler, typically discrete or combinatorial, process. This method has been used with great success in the theory of interacting particle systems, stochastic partial differential equations, mathematical genetics and stochastic population biology. In the last years, many important break throughs have been achieved, especially on a methodological level. However, often when trying to find dual processes one is restricited to ad-hoc methods. This project has three main objectives. First of all, we would like to transfer several concrete questions about certain SPDEs to questions about their dual processes (I). Secondly, we are interested in the longterm properties of the dual processes itself (II). Finally, we aim at a systematic analysis of the method of duality focussing on applicability, extending its scope and properties that are preserved under different types of duality (III).
对偶方法是一种数学形式主义,它允许找到两个不一定相关的随机过程的某些属性之间的密切联系,例如矩或长期行为。通常,通过分析一个简单的,通常是离散的或组合的过程的性质,可以研究一个复杂的随机过程的重要性质,例如由随机微分方程描述的随机过程。该方法已在相互作用粒子系统理论、随机偏微分方程、数学遗传学和随机种群生物学中获得了巨大成功。在过去几年中,取得了许多重大突破,特别是在方法层面上。然而,当试图找到双重过程时,往往会被限制到ad-hoc方法。该项目有三个主要目标。首先,我们想把关于某些SPDE的几个具体问题转移到关于它们的双重过程的问题上(I)。其次,我们感兴趣的是对偶过程本身的长期性质(II)。最后,我们的目标是系统地分析的方法的对偶集中在适用性,扩大其范围和属性,保留在不同类型的对偶(III)。

项目成果

期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On the notion(s) of duality for Markov processes
  • DOI:
    10.1214/12-ps206
  • 发表时间:
    2014-01-01
  • 期刊:
  • 影响因子:
    1.6
  • 作者:
    Jansen, Sabine;Kurt, Noemi
  • 通讯作者:
    Kurt, Noemi
Genetic Variability Under the Seedbank Coalescent
  • DOI:
    10.1534/genetics.115.176818
  • 发表时间:
    2015-07-01
  • 期刊:
  • 影响因子:
    3.3
  • 作者:
    Blath, Jochen;Casanova, Adrian Gonzalez;Wilke-Berenguer, Maite
  • 通讯作者:
    Wilke-Berenguer, Maite
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Professor Dr. Jochen Blath其他文献

Professor Dr. Jochen Blath的其他文献

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{{ truncateString('Professor Dr. Jochen Blath', 18)}}的其他基金

The role of dormancy in population genetics
休眠在群体遗传学中的作用
  • 批准号:
    285659567
  • 财政年份:
    2015
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes
Interacting stochastic (partial) differential equations, combinatorial stochastic processes and duality in spatial population dynamics
空间群体动态中的相互作用随机(偏)微分方程、组合随机过程和对偶性
  • 批准号:
    221756484
  • 财政年份:
    2012
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes

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