Distribution dependent SDEs driven by fractional Brownian motions

Fan X, Huang X, Suo Y, Yuan C (2022)
Stochastic Processes and their Applications 151: 23-67.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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DOI
Autor*in
Fan, XiliangUniBi; Huang, Xing; Suo, Yongqiang; Yuan, Chenggui
Einrichtung
Fakultät für Mathematik
Abstract / Bemerkung
In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H is an element of (0, 1/2)boolean OR(1/2, 1). We prove the well-posedness of this type equations, and then establish a general result on the Bismut formula for the Lions derivative by using Malliavin calculus. As applications, we provide the Bismut formulas of this kind for both non-degenerate and degenerate cases, and obtain the estimates of the Lions derivative and the total variation distance between the laws of two solutions.
Stichworte
Distribution dependent SDE; Fractional Brownian motion; Bismut type; formula; Lions derivative; Wasserstein distance
Erscheinungsjahr
2022
Zeitschriftentitel
Stochastic Processes and their Applications
Band
151
Seite(n)
23-67
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2979044

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Fan X, Huang X, Suo Y, Yuan C. Distribution dependent SDEs driven by fractional Brownian motions. Stochastic Processes and their Applications. 2022;151:23-67.
Fan, X., Huang, X., Suo, Y., & Yuan, C. (2022). Distribution dependent SDEs driven by fractional Brownian motions. Stochastic Processes and their Applications, 151, 23-67. https://doi.org/10.1016/j.spa.2022.05.007
Fan, Xiliang, Huang, Xing, Suo, Yongqiang, and Yuan, Chenggui. 2022. “Distribution dependent SDEs driven by fractional Brownian motions”. Stochastic Processes and their Applications 151: 23-67.
Fan, X., Huang, X., Suo, Y., and Yuan, C. (2022). Distribution dependent SDEs driven by fractional Brownian motions. Stochastic Processes and their Applications 151, 23-67.
Fan, X., et al., 2022. Distribution dependent SDEs driven by fractional Brownian motions. Stochastic Processes and their Applications, 151, p 23-67.
X. Fan, et al., “Distribution dependent SDEs driven by fractional Brownian motions”, Stochastic Processes and their Applications, vol. 151, 2022, pp. 23-67.
Fan, X., Huang, X., Suo, Y., Yuan, C.: Distribution dependent SDEs driven by fractional Brownian motions. Stochastic Processes and their Applications. 151, 23-67 (2022).
Fan, Xiliang, Huang, Xing, Suo, Yongqiang, and Yuan, Chenggui. “Distribution dependent SDEs driven by fractional Brownian motions”. Stochastic Processes and their Applications 151 (2022): 23-67.
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