Analysis of multidimensional processes
多维过程分析
基本信息
- 批准号:0601783
- 负责人:
- 金额:$ 19.2万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-05-01 至 2010-04-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Problems in two areas of probability are considered. The first is concerned with uniqueness for the solutions of stochasticdifferential equations arising from the areas of stochastic partialdifferential equations, measure-valued branching diffusions with branchingand spatial interactions, equations that depend on the past, and equations corresponding to degenerate elliptic operators.These are typically infinite-dimensional systems of equations, often with coefficients that degenerate at a boundary. The second area of research concerns Harnack inequalities and heat kernel estimates. An attempt will be made to characterize the Harnack inequality in both continuous models and ones with jumps. In addition regularity of solutions to equations associated with non-local operators in bounded regions will be investigated.In recent years researchers in mathematical physics, economics, andmathematical finance have realized that to adequately model real-worldphenomena, the possibility of jumps must be allowed. For example, anunexpected discovery or unexpected regional conflict might cause a sudden jumpup or down in stock prices. However, some of the very basic questionsabout models that incorporate jumps are as yet unanswered. One of the areasto be investigated is the regularity of such models. A typical question is:if the initial data is perturbed slightly, is it true that the behavior of the model at future times will also be only slightly perturbed? There are similar unanswered questions for certain models that originate in mathematicalbiology. In these cases the difficulty is not the presence of jumps, butthe presence of huge numbers of individuals and the possible interactionsbetween individuals.
在两个领域的概率问题被认为是。第一个是关于随机偏微分方程的解的唯一性,随机偏微分方程,具有分支和空间相互作用的测度值分支扩散,依赖于过去的方程,以及对应于退化椭圆算子的方程,这些都是典型的无限维方程组,通常具有在边界退化的系数。 第二个研究领域涉及Harnack不等式和热核估计。将尝试在连续模型和跳跃模型中刻画Harnack不等式。此外,我们还将研究与非局部算子相关的方程在有界区域中解的正则性,近年来,数学物理学、经济学和数学金融学的研究人员已经认识到,要充分模拟现实世界的现象,必须允许跳跃的可能性。例如,一个意想不到的发现或意想不到的地区冲突可能会导致股票价格突然上涨或下跌。然而,一些关于包含跳跃的模型的非常基本的问题还没有答案。其中一个有待研究的领域是这些模型的规律性。一个典型的问题是:如果初始数据受到轻微扰动,那么模型在未来的行为是否也只会受到轻微扰动? 对于起源于植物生物学的某些模型,也有类似的未回答的问题。在这些情况下,困难不在于跳跃的存在,而在于大量个体的存在以及个体之间可能的相互作用。
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)
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Richard Bass其他文献
The A, ASC, and L systems for the transport of amino acids in Chinese hamster ovary cells (CHO-K1).
中国仓鼠卵巢细胞 (CHO-K1) 中转运氨基酸的 A、ASC 和 L 系统。
- DOI:
- 发表时间:
1981 - 期刊:
- 影响因子:4.8
- 作者:
Richard Bass;Holly;B. HedegaardS;Larry Dillehayg;John Moffett;Ellis Englesberga - 通讯作者:
Ellis Englesberga
Allergen Vial Mixing and Immunotherapy: Risks of Infections and Vial Contamination
过敏原小瓶混合和免疫治疗:感染和小瓶污染的风险
- DOI:
- 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
P. C. Lay;Richard Bass;Sandra Y. Lin - 通讯作者:
Sandra Y. Lin
The martingales of an independent increment process
- DOI:
10.1016/0304-4149(79)90045-0 - 发表时间:
1979-12-01 - 期刊:
- 影响因子:
- 作者:
Richard Bass - 通讯作者:
Richard Bass
The site for catabolite deactivation in the L-arabinose BAD operon in Escherichia coli B/r
- DOI:
10.1007/bf00416978 - 发表时间:
1976-10-01 - 期刊:
- 影响因子:2.600
- 作者:
Richard Bass;Laurel Heffernan;Katherine Sweadner;Ellis Englesberg - 通讯作者:
Ellis Englesberg
Richard Bass的其他文献
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{{ truncateString('Richard Bass', 18)}}的其他基金
Stochastic differential equations: potential theory and uniqueness
随机微分方程:势论和唯一性
- 批准号:
0901505 - 财政年份:2009
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
Mathematical Sciences: Brownian Motion and Related Processes
数学科学:布朗运动及相关过程
- 批准号:
9322689 - 财政年份:1994
- 资助金额:
$ 19.2万 - 项目类别:
Continuing Grant
ENG/INT Joint Grant Opportunities For Collaborative Research at Foreign Centers of Excellence: Electric Vehicles Infrastructure
ENG/INT 国外卓越中心合作研究联合资助机会:电动汽车基础设施
- 批准号:
9412636 - 财政年份:1994
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
Mathematical Sciences: Seminar on Stohastic Processes; Seattle, Washington, March 26-28, 1992
数学科学:随机过程研讨会;
- 批准号:
9119558 - 财政年份:1992
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
Mathematical Sciences: Brownian Motion and Diffusions
数学科学:布朗运动和扩散
- 批准号:
9100244 - 财政年份:1991
- 资助金额:
$ 19.2万 - 项目类别:
Continuing Grant
US-UK Cooperative Research: Diffusions on Fractals
美英合作研究:分形扩散
- 批准号:
8921538 - 财政年份:1990
- 资助金额:
$ 19.2万 - 项目类别:
Standard Grant
Mathematical Sciences: Stochastic Processes
数学科学:随机过程
- 批准号:
8822053 - 财政年份:1989
- 资助金额:
$ 19.2万 - 项目类别:
Continuing Grant
Mathematical Sciences: Stochastic Processes
数学科学:随机过程
- 批准号:
8701073 - 财政年份:1987
- 资助金额:
$ 19.2万 - 项目类别:
Continuing Grant
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