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 et Modèles Aléatoires
National Research University
Université d'Evry Val d'Essonne

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

15 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	849-898
Number of pages	50
Journal	Discrete and Continuous Dynamical Systems
Volume	41
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2020302
Publication status	Published - 1 Jan 2020
Externally published	Yes

Keywords

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

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10.3934/dcds.2020302

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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",

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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

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DO - 10.3934/dcds.2020302

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VL - 41

SP - 849

EP - 898

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 2

ER -

WELL-POSEDNESS of SOME NON-LINEAR STABLE DRIVEN SDES

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Keywords

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