Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos

Young Pil Choi; Samir Salem

doi:10.1016/j.jde.2018.10.042

Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos

Young Pil Choi, Samir Salem

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov–Fokker–Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.

Original language	English
Pages (from-to)	6109-6148
Number of pages	40
Journal	Journal of Differential Equations
Volume	266
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2018.10.042
Publication status	Published - 2019 Apr 15

Bibliographical note

Funding Information:
The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735 ) and POSCO Science Fellowship of POSCO TJ Park Foundation . SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris Sciences et Lettres .

Funding Information:
The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris Sciences et Lettres.

Publisher Copyright:
© 2018 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2018.10.042

Cite this

@article{a824314738bd4868b2e205d0da6f04e3,

title = "Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos",

abstract = "We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov–Fokker–Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.",

author = "Choi, {Young Pil} and Samir Salem",

note = "Funding Information: The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735 ) and POSCO Science Fellowship of POSCO TJ Park Foundation . SS was supported by the Fondation des Sciences Math{\'e}matiques de Paris and Universit{\'e} Paris Sciences et Lettres . Funding Information: The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Math{\'e}matiques de Paris and Universit{\'e} Paris Sciences et Lettres. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = apr,

day = "15",

doi = "10.1016/j.jde.2018.10.042",

language = "English",

volume = "266",

pages = "6109--6148",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "9",

}

TY - JOUR

T1 - Collective behavior models with vision geometrical constraints

T2 - Truncated noises and propagation of chaos

AU - Choi, Young Pil

AU - Salem, Samir

N1 - Funding Information: The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735 ) and POSCO Science Fellowship of POSCO TJ Park Foundation . SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris Sciences et Lettres . Funding Information: The authors warmly thank Professor Maxime Hauray for helpful discussion and valuable comments. YPC was supported by NRF grant (no. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris Sciences et Lettres. Publisher Copyright: © 2018 Elsevier Inc.

PY - 2019/4/15

Y1 - 2019/4/15

N2 - We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov–Fokker–Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.

AB - We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov–Fokker–Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.

UR - http://www.scopus.com/inward/record.url?scp=85056209655&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056209655&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2018.10.042

DO - 10.1016/j.jde.2018.10.042

M3 - Article

AN - SCOPUS:85056209655

SN - 0022-0396

VL - 266

SP - 6109

EP - 6148

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this