Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts
Wu M, Hao Z (2023)
Stochastic Processes and their Applications 164: 416-442.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Wu, Mingyan;
Hao, ZimoUniBi
Einrichtung
Abstract / Bemerkung
In this paper, we show the weak and strong well-posedness of density dependent stochastic differential equations driven by & alpha;-stable processes with & alpha; & ISIN; (1, 2). The existence part is based on Euler's approximation as Hao et al. (2021), while, the uniqueness is based on the Schauder estimates in Besov spaces for nonlocal Fokker-Planck equations. For the existence, we only assume the drift being continuous in the density variable. For the weak uniqueness, the drift is assumed to be Lipschitz in the density variable, while for the strong uniqueness, we also need to assume the drift being /30-order Holder continuous in the spatial variable, where /30 & ISIN; (1 - & alpha;/2, 1). & COPY; 2023 Elsevier B.V. All rights reserved.
Stichworte
Levy process;
Density dependent SDE;
Heat kernel;
Schauder's estimate
Erscheinungsjahr
2023
Zeitschriftentitel
Stochastic Processes and their Applications
Band
164
Seite(n)
416-442
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2983731
Zitieren
Wu M, Hao Z. Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts. Stochastic Processes and their Applications. 2023;164:416-442.
Wu, M., & Hao, Z. (2023). Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts. Stochastic Processes and their Applications, 164, 416-442. https://doi.org/10.1016/j.spa.2023.07.016
Wu, Mingyan, and Hao, Zimo. 2023. “Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts”. Stochastic Processes and their Applications 164: 416-442.
Wu, M., and Hao, Z. (2023). Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts. Stochastic Processes and their Applications 164, 416-442.
Wu, M., & Hao, Z., 2023. Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts. Stochastic Processes and their Applications, 164, p 416-442.
M. Wu and Z. Hao, “Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts”, Stochastic Processes and their Applications, vol. 164, 2023, pp. 416-442.
Wu, M., Hao, Z.: Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts. Stochastic Processes and their Applications. 164, 416-442 (2023).
Wu, Mingyan, and Hao, Zimo. “Well-posedness of density dependent SDE driven by a-stable process with Hölder drifts”. Stochastic Processes and their Applications 164 (2023): 416-442.
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