WELL-POSEDNESS OF SOME NON-LINEAR STABLE DRIVEN SDES

NOUFEL FRIKHA; VALENTIN KONAKOV; STEPHANE MENOZZI

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WELL-POSEDNESS OF SOME NON-LINEAR STABLE DRIVEN SDES

机译：一些非线性稳定驱动的SDES良好

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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 Levy processes with values in R~d under some mild Holder 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.

机译：在漂移和扩散系数上的一些温和的保持器规则假设下，通过非退化对称α稳定的征收过程，在McKean-Vlasov的某些非线性对称α-稳定的征收过程中提供了一些非线性随机微分方程的良好。关于空间和测量变量。这里开发的方法允许即使在所谓的超批判性情况下也可以考虑无界漂移术语，即稳定性指数α∈（0,1）。新的强大良好的良好结果也来自于之前的分析。

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《Discrete and continuous dynamical systems》 |2021年第2期|849-898|共50页
作者
NOUFEL FRIKHA; VALENTIN KONAKOV; STEPHANE MENOZZI;
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作者单位

Universite de Paris Laboratoire de Probabilites Statistiques et Modelisation (LPSM) UMR 8001 F-75013 Paris France;

Laboratory of Stochastic Analysis Higher School of Economics Pokrovsky boulevard 11 Moscow Russian Federation;

Laboratoire de Modelisation Mathematique d'Evry (LaMME) UMR CNRS 8070 Universite d'Evry Val d'Essonne Universite Paris-Saclay 23 Boulevard de France 91037 Evry France Laboratory of Stochastic Analysis Higher School of Economics Pokrovsky boulevard 11 Moscow Russian Federation;

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正文语种 eng
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关键词
McKean-Vlasov stable SDEs; non-linear martingale problem; weak uniqueness; strong uniqueness; perturbative techniques of parametrix type;

机译：McKean-Vlasov稳定SDES;非线性鞅问题;唯一性;强烈的唯一性;parametrix类型的扰动技术;

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WELL-POSEDNESS OF SOME NON-LINEAR STABLE DRIVEN SDES

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