STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE

Friesen M, Kutovyi O (2020)
KINETIC AND RELATED MODELS 13(2): 211-247.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Friesen, Martin; Kutovyi, OleksandrUniBi
Abstract / Bemerkung
We present a stochastic version of the Cucker-Smale flocking dynamics described by a system of N interacting particles. The velocity aligment of particles is purely discontinuous with unbounded and, in general, non-Lipschitz continuous interaction rates. Performing the mean-field limit as N -> infinity we identify the limiting process with a solution to a nonlinear martingale problem associated with a McKean-Vlasov stochastic equation with jumps. Moreover, we show uniqueness and stability for the kinetic equation by estimating its solutions in the total variation and Wasserstein distance. Finally, we prove uniqueness in law for the McKean-Vlasov equation, i.e. we establish propagation of chaos.
Stichworte
Flocking; Cucker-Smale dynamics; mean-field equation; McKean-Vlasov; stochastic equation; propagation of chaos; Total variation distance; Wasserstein distance
Erscheinungsjahr
2020
Zeitschriftentitel
KINETIC AND RELATED MODELS
Band
13
Ausgabe
2
Seite(n)
211-247
ISSN
1937-5093
eISSN
1937-5077
Page URI
https://pub.uni-bielefeld.de/record/2940696

Zitieren

Friesen M, Kutovyi O. STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE. KINETIC AND RELATED MODELS. 2020;13(2):211-247.
Friesen, M., & Kutovyi, O. (2020). STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE. KINETIC AND RELATED MODELS, 13(2), 211-247. doi:10.3934/krm.2020008
Friesen, M., and Kutovyi, O. (2020). STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE. KINETIC AND RELATED MODELS 13, 211-247.
Friesen, M., & Kutovyi, O., 2020. STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE. KINETIC AND RELATED MODELS, 13(2), p 211-247.
M. Friesen and O. Kutovyi, “STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE”, KINETIC AND RELATED MODELS, vol. 13, 2020, pp. 211-247.
Friesen, M., Kutovyi, O.: STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE. KINETIC AND RELATED MODELS. 13, 211-247 (2020).
Friesen, Martin, and Kutovyi, Oleksandr. “STOCHASTIC CUCKER-SMALE FLOCKING DYNAMICS OF JUMP-TYPE”. KINETIC AND RELATED MODELS 13.2 (2020): 211-247.