Coupled McKean-Vlasov stochastic differential equations with jumps
Probability
2020-08-07 v2
Abstract
This work concerns a type of coupled McKean-Vlasov stochastic differential equations (MVSDEs in short) with jumps. First, we prove superposition principles for these coupled MVSDEs with jumps and non-local space-distribution dependent Fokker-Planck equations. Since superposition principles are related to the well-posedness of weak solutions for coupled MVSDEs with jumps, then we give some conditions to assure it. After this, we construct space-distribution valued Markov processes associated with these coupled MVSDEs with jumps. Finally, the ergodicity of these coupled MVSDEs with jumps are investigated. As a by-product, we show the exponential ergodicity for a type of MVSDEs with jumps.
Keywords
Cite
@article{arxiv.2005.13036,
title = {Coupled McKean-Vlasov stochastic differential equations with jumps},
author = {Huijie Qiao},
journal= {arXiv preprint arXiv:2005.13036},
year = {2020}
}
Comments
Some results are similar to that in [21]