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Mathematics > Probability

arXiv:1812.05026 (math)
[Submitted on 12 Dec 2018]

Title:A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with Lévy jumps

Authors:Ankush Agarwal, Stefano Pagliarani
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Abstract:We consider a class of Lévy-driven stochastic differential equations (SDEs) with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed that the coefficient is bounded, affine in the state variable, and only measurable in the law of the solution. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration scheme that approximates the law of the solution through its characteristic function. Numerical illustrations show the effectiveness of our method, which appears to be appropriate to handle the multi-dimensional setting.
Subjects: Probability (math.PR)
MSC classes: 65C30, 65T99, 65Q20
Cite as: arXiv:1812.05026 [math.PR]
  (or arXiv:1812.05026v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.05026

Submission history

From: Ankush Agarwal [view email]
[v1] Wed, 12 Dec 2018 16:54:16 UTC (52 KB)
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