WELL-POSEDNESS of SOME NON-LINEAR STABLE DRIVEN SDES

Noufel Frikha; Valentin Konakov; Stéphane Menozzi

doi:10.3934/dcds.2020302

WELL-POSEDNESS of SOME NON-LINEAR STABLE DRIVEN SDES

Noufel Frikha
, Valentin Konakov
, Stéphane Menozzi

Laboratoire de Probabilités Statistiques et Modélisation (LPSM)
Laboratoire de Probabilités et Modèles Aléatoires
Laboratory of Stochastic Analysis
National Research University
Université d'Evry Val d'Essonne

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

15 Citations (Scopus)

Résumé

We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric α-stable Lévy processes with values in R^d under some mild Hölder regularity assumptions on the drift and diffusion coefficients with respect to both space and measure variables. The methodology developed here allows to consider unbounded drift terms even in the so-called super-critical case, i.e. when the stability index α ∈ (0, 1). New strong well-posedness results are also derived from the previous analysis.

langue originale	Anglais
Pages (de - à)	849-898
Nombre de pages	50
journal	Discrete and Continuous Dynamical Systems- Series A
Volume	41
Numéro de publication	2
Les DOIs	https://doi.org/10.3934/dcds.2020302
état	Publié - 1 janv. 2020
Modification externe	Oui

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title = "WELL-POSEDNESS of SOME NON-LINEAR STABLE DRIVEN SDES",

abstract = "We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric α-stable L{\'e}vy processes with values in Rd under some mild H{\"o}lder regularity assumptions on the drift and diffusion coefficients with respect to both space and measure variables. The methodology developed here allows to consider unbounded drift terms even in the so-called super-critical case, i.e. when the stability index α ∈ (0, 1). New strong well-posedness results are also derived from the previous analysis.",

keywords = "McKean-Vlasov stable SDEs, Non-linear martingale problem, Perturbative techniques of parametrix type, Strong uniqueness, Weak uniqueness",

author = "Noufel Frikha and Valentin Konakov and St{\'e}phane Menozzi",

year = "2020",

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T1 - WELL-POSEDNESS of SOME NON-LINEAR STABLE DRIVEN SDES

AU - Frikha, Noufel

AU - Konakov, Valentin

AU - Menozzi, Stéphane

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric α-stable Lévy processes with values in Rd under some mild Hölder regularity assumptions on the drift and diffusion coefficients with respect to both space and measure variables. The methodology developed here allows to consider unbounded drift terms even in the so-called super-critical case, i.e. when the stability index α ∈ (0, 1). New strong well-posedness results are also derived from the previous analysis.

AB - We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric α-stable Lévy processes with values in Rd under some mild Hölder regularity assumptions on the drift and diffusion coefficients with respect to both space and measure variables. The methodology developed here allows to consider unbounded drift terms even in the so-called super-critical case, i.e. when the stability index α ∈ (0, 1). New strong well-posedness results are also derived from the previous analysis.

KW - McKean-Vlasov stable SDEs

KW - Non-linear martingale problem

KW - Perturbative techniques of parametrix type

KW - Strong uniqueness

KW - Weak uniqueness

UR - https://www.scopus.com/pages/publications/85094322202

U2 - 10.3934/dcds.2020302

DO - 10.3934/dcds.2020302

M3 - Article

AN - SCOPUS:85094322202

SN - 1078-0947

VL - 41

SP - 849

EP - 898

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 2

ER -

WELL-POSEDNESS of SOME NON-LINEAR STABLE DRIVEN SDES

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