Stochastic Spatial Processes
随机空间过程
基本信息
- 批准号:0505439
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2005
- 资助国家:美国
- 起止时间:2005-07-01 至 2008-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This proposal will address questions in the theory of interacting particle systems and stochastic spatial processes. These stochastic processes are models for large systems with many interacting ``components'' (cells, individuals, particles, plants, etc.). Some examples of the phenomena these systems model are: competition of species, epidemics, population growth, evolution of genetic traits. A principal goal of research in this area is to understand how the macroscopic behavior of large systems depends on the individual interactions between components. Two competition models will be studied, a spatial stochastic Lotka-Volterra model and a multitype contact process. For the Lotka-Volterra model, the objectives are to determine the parameter regions which correspond to survival of one species and coexistence of both species. The project is part of the investigator's ongoing efforts to understand and exploit the scaling relationship between interacting particle systems and measure-valued diffusions. For the multitype contact process, the questions of interest concern survival versus extinction on regular trees. The investigator expects to find new phase dependent survival and extinction phenomena that do not exist in the lattice case. A second general area of this proposal addresses problems motivated by population genetics. The evolution of genetic traits in geographically structured populations is often modeled with Kimura's stepping stone model, where questions about measures of kinship are reformulated in terms of questions about the behavior of coalescing random walk systems. The investigator's previous research includes work on limit theorems for these systems on large, two-dimensional lattice sets with torus or wrap-around boundary conditions. The goal here is to show robustness of these theorems over a wide range of boundary conditions, justifying their use in population genetics.This proposal involves research in the theory of interacting particle systems and stochastic spatial processes. These stochastic processes are models for large systems with many interacting components (cells, individuals, particles, plants, etc.). The goal of this research is to obtain a better qualitative understanding of various complex phenomena that interacting particles systems model well, such as models of: competition of species, epidemics, population growth, evolution of genetic traits. A principal goal of research in this area is to understand how the macroscopic behavior of large systems depends on the individual interactions between components. Several specific models will be studied, including a stochastic spatial version of a well known model for competition between species. In addition to work on specific models, the investigator will try to extend the validity of some approximation theorems established for some specific models to handle more general ones, thus justifying their use in applications.
这个建议将解决相互作用粒子系统和随机空间过程理论中的问题。 这些随机过程是具有许多相互作用的“组件”(细胞、个体、粒子、植物等)的大型系统的模型。 这些系统模型的一些现象的例子是:物种竞争,流行病,人口增长,遗传性状的进化。这一领域研究的一个主要目标是了解大系统的宏观行为如何依赖于组件之间的个体相互作用。 两个竞争模型将被研究,空间随机Lotka-Volterra模型和多类型接触过程。 对于Lotka-Volterra模型,目标是确定对应于一个物种生存和两个物种共存的参数区域。该项目是研究人员正在进行的努力的一部分,以了解和利用相互作用的粒子系统和测量值扩散之间的标度关系。对于多型接触过程,感兴趣的问题是关于规则树的生存与灭绝。研究者期望发现新的相依赖的生存和灭绝现象,不存在于晶格的情况下。该建议的第二个一般领域涉及群体遗传学引起的问题。地理结构种群中遗传性状的进化通常采用木村的垫脚石模型(英语:Stepping stone model)来建模,其中关于亲属关系的度量的问题被重新表述为关于合并随机游走系统行为的问题。 研究者以前的研究包括这些系统的极限定理的工作,大型,二维格集环面或环绕边界条件。 这里的目标是显示这些定理在广泛的边界条件下的鲁棒性,证明它们在群体遗传学中的应用是合理的。 这些随机过程是具有许多相互作用的组件(细胞,个体,粒子,植物等)的大型系统的模型。 本研究的目标是更好地定性了解相互作用粒子系统模型的各种复杂现象,例如:物种竞争,流行病,人口增长,遗传性状进化。 这一领域研究的一个主要目标是了解大系统的宏观行为如何依赖于组件之间的个体相互作用。几个具体的模型将进行研究,包括一个众所周知的物种之间的竞争模型的随机空间版本。除了工作在特定的模型,调查人员将试图延长的有效性,为一些特定的模型建立一些近似定理,以处理更一般的,从而证明他们在应用中的使用。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
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 }}
J. Theodore Cox其他文献
Recurrence and ergodicity of interacting particle systems
相互作用粒子系统的循环性和遍历性
- DOI:
- 发表时间:
2002 - 期刊:
- 影响因子:0
- 作者:
J. Theodore Cox;A. Klenke - 通讯作者:
A. Klenke
Occupation time large deviations of the voter model
- DOI:
10.1007/bf00319297 - 发表时间:
1988-03-01 - 期刊:
- 影响因子:1.600
- 作者:
Maury Bramson;J. Theodore Cox;David Griffeath - 通讯作者:
David Griffeath
Consolidation rates for two interacting systems in the plane
- DOI:
10.1007/bf00324856 - 发表时间:
1986-11-01 - 期刊:
- 影响因子:1.600
- 作者:
Maury Bramson;J. Theodore Cox;David Griffeath - 通讯作者:
David Griffeath
Evolutionary Games on the Torus with Weak Selection
环面弱选择的进化博弈
- DOI:
- 发表时间:
2015 - 期刊:
- 影响因子:0
- 作者:
J. Theodore Cox;R. Durrett - 通讯作者:
R. Durrett
Weak atomic convergence of finite voter models toward Fleming–Viot processes
- DOI:
10.1016/j.spa.2017.09.015 - 发表时间:
2018-07-01 - 期刊:
- 影响因子:
- 作者:
Yu-Ting Chen;J. Theodore Cox - 通讯作者:
J. Theodore Cox
J. Theodore Cox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('J. Theodore Cox', 18)}}的其他基金
Joint U.S.-Brazil Research in Interacting Particle Systems
美国-巴西相互作用粒子系统联合研究
- 批准号:
9600698 - 财政年份:1996
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Sciences: Stochastic Spatial Models
数学科学:随机空间模型
- 批准号:
9303233 - 财政年份:1993
- 资助金额:
-- - 项目类别:
Continuing Grant
U.S.-Brazil Cooperative Science Program: Latin American Congress in Probability & Mathematical Statistics; Sao Paulo, Brazil; June 28-July 3, 1993
美国-巴西合作科学计划:拉丁美洲概率大会
- 批准号:
9301461 - 财政年份:1993
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Sciences: Interacting Particle Systems
数学科学:相互作用的粒子系统
- 批准号:
8802055 - 财政年份:1988
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Sciences: Interacting Particle Systems
数学科学:相互作用的粒子系统
- 批准号:
8601713 - 财政年份:1986
- 资助金额:
-- - 项目类别:
Continuing Grant
相似国自然基金
高铁对欠发达省域国土空间协调(Spatial Coherence)影响研究与政策启示-以江西省为例
- 批准号:52368007
- 批准年份:2023
- 资助金额:32 万元
- 项目类别:地区科学基金项目
高铁影响空间失衡(Spatial Inequality)的多尺度变异机理的理论和实证研究
- 批准号:51908258
- 批准年份:2019
- 资助金额:26.0 万元
- 项目类别:青年科学基金项目
相似海外基金
Stochastic Spatial Processes
随机空间过程
- 批准号:
RGPIN-2019-03928 - 财政年份:2022
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Stochastic Spatial Processes
随机空间过程
- 批准号:
RGPIN-2019-03928 - 财政年份:2021
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Stochastic Spatial Processes
随机空间过程
- 批准号:
RGPIN-2019-03928 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Stochastic Spatial Processes
随机空间过程
- 批准号:
RGPIN-2019-03928 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Discovery Grants Program - Individual
Statistical analysis of tempo-spatial stochastic integral processes
时空随机积分过程的统计分析
- 批准号:
322862354 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
Stochastic spatial coagulation particle processes (C08)
随机空间凝固粒子过程 (C08)
- 批准号:
259773680 - 财政年份:2014
- 资助金额:
-- - 项目类别:
Collaborative Research Centres
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
Stochastic processes with spatial constraints
具有空间约束的随机过程
- 批准号:
1007823 - 财政年份:2010
- 资助金额:
-- - 项目类别:
Standard Grant