Reaction-Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations

被引：1

作者：

da Costa, Conrado ^{[1
]}

Paulo da Costa, Bernardo Freitas ^{[2
]}

Valesin, Daniel ^{[3
]}

机构：

[1] Univ Durham, Dept Math Sci, Math Sci & Comp Sci Bldg,Upper Mountjoy Campus, Durham DH1 3LE, England

[2] Univ Fed Rio de Janeiro, Inst Matemat, Ctr Tecnol Bloco C,Av Athos Silveira Ramos 149, Rio De Janeiro, RJ, Brazil

[3] Univ Groningen, Bernoulli Inst, Nijenborgh 9, NL-9747 AG Groningen, Netherlands

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 02期

关键词：

Reaction-diffusion models; Scaling limits of particle systems; Martingale problems; Thermodynamic limit;

D O I：

10.1007/s10959-022-01187-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish the existence of solutions to a class of nonlinear stochastic differential equations of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained is the scaling limit of a sequence of interacting particle systems and satisfies the martingale problem corresponding to the target differential equation.

引用

页码：1059 / 1087

页数：29

共 50 条

[1] Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations
Conrado da Costa
Bernardo Freitas Paulo da Costa
Daniel Valesin
[J]. Journal of Theoretical Probability, 2023, 36 : 1059 - 1087
[2] Finite and Infinite-Dimensional Attractors of Multivalued Reaction-Diffusion Equations
J. Valero
[J]. Acta Mathematica Hungarica, 2000, 88 : 239 - 258
[3] Finite and infinite-dimensional attractors of multivalued reaction-diffusion equations
Valero, J
[J]. ACTA MATHEMATICA HUNGARICA, 2000, 88 (03) : 239 - 258
[4] Infinite-Dimensional Stochastic Differential Equations with Symmetry
Osada, Hirofumi
[J]. STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND RELATED FIELDS: IN HONOR OF MICHAEL ROCKNER, SPDERF, 2018, 229 : 549 - 559
[5] Stability of a class of nonlinear reaction-diffusion equations and stochastic homogenization
Hafsa, Omar Anza
Mandallena, Jean Philippe
Michaille, Gerard
[J]. ASYMPTOTIC ANALYSIS, 2019, 115 (3-4) : 169 - 221
[6] Parameter estimation in infinite-dimensional stochastic differential equations
Kim, YT
[J]. STATISTICS & PROBABILITY LETTERS, 1999, 45 (03) : 195 - 204
[7] Infinite-dimensional stochastic differential equations and tail σ-fields
Osada, Hirofumi
Tanemura, Hideki
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2020, 177 (3-4) : 1137 - 1242
[8] Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation
Efendiev, M
Miranville, A
Zelik, S
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2004, 460 (2044): : 1107 - 1129
[9] NONLINEAR EQUATIONS WITH ESSENTIALLY INFINITE-DIMENSIONAL DIFFERENTIAL OPERATORS
Bohdans'kyi, Yu. V.
Statkevych, V. M.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2011, 62 (11) : 1822 - 1827
[10] Nonlinear equations with essentially infinite-dimensional differential operators
Yu. V. Bohdans’kyi
V. M. Statkevych
[J]. Ukrainian Mathematical Journal, 2011, 62 : 1822 - 1827

← 1 2 3 4 5 →