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Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations / Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 296, number 1481 (April 2024)Publisher: Providence : American Mathematical Society, April 2024Description: v, 90 SeitenISBN:
  • 9781470467012
Subject(s): Additional physical formats: 9781470478186 | Erscheint auch als: Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations. Online-Ausgabe 1st ed. Providence : American Mathematical Society, 2024. 1 online resource (102 pages) | Erscheint auch als: Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations. Online-Ausgabe Providence : American Mathematical Society, 2024. 1 Online-Ressource (v, 90 Seiten)DDC classification:
  • 519.2/2 23/eng20240823
MSC: MSC: 60H10LOC classification:
  • QA274.23
Summary: "Recently, Hairer et al. (2015) showed that there exist stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong Lp-sense with respect to the initial value for every p (0,]. In this article we provide conditions on the coefficient functions of the SDE and on p (0,] that are sufficient for local Lipschitz continuity in the strong Lp-sense with respect to the initial value and we establish explicit estimates for the local Lipschitz continuity constants. In particular, we prove local Lipschitz continuity in the initial value for several nonlinear stochastic ordinary and stochastic partial differential equations in the literature such as the stochastic van der Pol oscillator, Brownian dynamics, the Cox-Ingersoll-Ross processes and the Cahn-Hilliard-Cook equation. As an application of our estimates, we obtain strong completeness for several nonlinear SDEs"--PPN: PPN: 1896766056
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-296.2024,1481 Nicht ausleihbar
Total holds: 0
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