Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach

被引：0

作者：

Kalinin, Alexander ^{[1
]}

Meyer-Brandis, Thilo ^{[1
]}

Proske, Frank ^{[2
]}

机构：

[1] Ludwig Maximilians Univ Munchen, Dept Math, D-80333 Munich, Germany

[2] Univ Oslo, Dept Math, N-0316 Oslo, Norway

来源：

STOCHASTICS AND DYNAMICS | 2024年 / 24卷 / 05期

关键词：

McKean-Vlasov equation; Lyapunov stability; moment estimate; asymptotic behavior; pathwise uniqueness; strong solution; non-Lipschitz coefficient; Ito process; STOCHASTIC DIFFERENTIAL-EQUATIONS; MEAN-FIELD GAMES; SYSTEMIC RISK; MODEL;

D O I：

10.1142/S0219493724500394

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic case, we also obtain the existence of unique strong solutions. By using our approach, which is based on an extension of the Yamada-Watanabe ansatz to the multidimensional setting and which does not rely on the construction of Lyapunov functions, we prove first moment and pathwise exponential stability. Furthermore, Lyapunov exponents are computed explicitly.

引用

页数：49

共 35 条

[11]

Carmona R, 2018, PROB THEOR STOCH MOD, V83, P3, DOI 10.1007/978-3-319-58920-6

[12]

Carmona R, 2018, PROB THEOR STOCH MOD, V84, P1, DOI 10.1007/978-3-319-56436-4

[13]

CARMONA R., 2014, STOCH ANAL APPL, V100, P77, DOI 10.1007/978- 3- 319- 11292- 3_4

[14] Systemic Risk and Stochastic Games with Delay [J].

Carmona, Rene ;

Fouque, Jean-Pierre ;

Mousavi, Seyyed Mostafa ;

Sun, Li-Hsien .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 179 (02) :366-399

[15] MEAN FIELD GAMES AND SYSTEMIC RISK [J].

Carmona, Rene ;

Fouque, Jean-Pierre ;

Sun, Li-Hsien .

COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2015, 13 (04) :911-933

[16] Control of McKean-Vlasov dynamics versus mean field games [J].

Carmona, Rene ;

Delarue, Francois ;

Lachapelle, Aime .

MATHEMATICS AND FINANCIAL ECONOMICS, 2013, 7 (02) :131-166

[17] PROBABILISTIC ANALYSIS OF MEAN-FIELD GAMES [J].

Carmona, Rene ;

Delarue, Francois .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (04) :2705-2734

[18]

Chiang T. S., 1994, SOOCHOW J MATH, V20, P507

[19]

Fouque JP, 2013, HANDBOOK ON SYSTEMIC RISK, P444

[20] Stability in a Model of Interbank Lending [J].

Fouque, Jean-Pierre ;

Ichiba, Tomoyuki .

SIAM JOURNAL ON FINANCIAL MATHEMATICS, 2013, 4 (01) :784-803

← 1 2 3 4 →