Annals of Applied Probability最新文献_第3页

A spatial measure-valued model for chemical reaction networks in heterogeneous systems 非均相系统中化学反应网络的空间测度值模型

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1904

Lea Popovic, Amandine Veber

引用次数: 3

Graphon mean field systems 石墨平均场系统

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1901

Erhan Bayraktar, Suman Chakraborty, Ruoyu Wu

引用次数: 33

Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling 扩散尺度下相互作用神经元系统收敛到平均场极限的强误差界

2区数学

Annals of Applied Probability Pub Date : 2023-10-01 DOI: 10.1214/22-aap1900

Xavier Erny, Eva Löcherbach, Dasha Loukianova

{"title":"Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling","authors":"Xavier Erny, Eva Löcherbach, Dasha Loukianova","doi":"10.1214/22-aap1900","DOIUrl":"https://doi.org/10.1214/22-aap1900","url":null,"abstract":"We consider the stochastic system of interacting neurons introduced in (J. Stat. Phys. 158 (2015) 866–902) and in (Ann. Inst. Henri Poincaré Probab. Stat. 52 (2016) 1844–1876) and then further studied in (Electron. J. Probab. 26 (2021) 20) in a diffusive scaling. The system consists of N neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the potential of the spiking neuron is reset to 0 and all other neurons receive an additional amount of potential which is a centred random variable of order 1/ N. In between successive spikes, each neuron’s potential follows a deterministic flow. In our previous article (Electron. J. Probab. 26 (2021) 20) we proved the convergence of the system, as N→∞, to a limit nonlinear jumping stochastic differential equation. In the present article we complete this study by establishing a strong convergence result, stated with respect to an appropriate distance, with an explicit rate of convergence. The main technical ingredient of our proof is the coupling introduced in (Z. Wahrsch. Verw. Gebiete 34 (1976) 33–58) of the point process representing the small jumps of the particle system with the limit Brownian motion.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135996637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

A unified approach to linear-quadratic-Gaussian mean-field team: Homogeneity, heterogeneity and quasi-exchangeability 线性二次高斯平均场组的统一方法:均匀性、非均匀性和准互换性

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-08-01 DOI: 10.1214/22-aap1878

Xinwei Feng, Ying Hu, Jianhui Huang

{"title":"A unified approach to linear-quadratic-Gaussian mean-field team: Homogeneity, heterogeneity and quasi-exchangeability","authors":"Xinwei Feng, Ying Hu, Jianhui Huang","doi":"10.1214/22-aap1878","DOIUrl":"https://doi.org/10.1214/22-aap1878","url":null,"abstract":"This paper aims to systematically solve stochastic team optimization of large-scale system, in linear-quadratic-Gaussian framework. Concretely, the underlying large-scale system involves considerable weakly-coupled cooperative agents for which the individual admissible controls: ( i ) enter the diffusion terms, ( ii ) are constrained in some closed-convex subsets, and ( iii ) subject to a general partial decentralized information structure. A more im-portant but serious feature: ( iv ) all agents are heterogenous with continuum instead of ﬁnite diversity. Combination of ( i )-( iv ) yields a quite general modeling of stochastic team-optimization, but on the other hand, also fails current existing techniques of team analysis. In particular, classical team consistency with continuum heterogeneity collapses because of ( i ). As the resolution, a novel uniﬁed approach is proposed under which the intractable continuum heterogeneity can be converted to a more tractable homogeneity . As a trade-off, the underlying randomness is augmented, and all agents become (quasi) weakly-exchangeable. Such approach essentially involves a subtle balance between homogeneity v.s. heterogeneity, and left (prior-sampling)-v.s. right (posterior-sampling) information ﬁltration. Subsequently, the consistency condition (CC) system takes a new type of forward-backward stochastic system with double-projections (due to ( ii ), ( iii )), along with spatial mean on continuum heterogenous index (due to ( iv )). Such system is new in team literature and its well-posedness is also challenging. We address this is-sue under mild conditions. Related asymptotic optimality is also established.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44814943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Phase transition for percolation on a randomly stretched square lattice 随机拉伸正方形晶格上渗流的相变

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-08-01 DOI: 10.1214/22-aap1887

Emy, Anchis, ugusto, eixeira

引用次数: 1

An SPDE approach to perturbation theory of Φ24: Asymptoticity and short distance behavior Φ24微扰理论的SPDE方法：渐近性和短距离行为

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-08-01 DOI: 10.1214/22-aap1873

Hao Shen, Rongchan Zhu, Xiangchan Zhu

引用次数: 5

Well-posedness and wave-breaking for the stochastic rotation-two-component Camassa–Holm system 随机旋转双分量Camassa-Holm系统的适定性和破波