Abstract
Buckdahn et al. (2009b) introduced a mean-field stochastic differential equation to study the backward stochastic differential equation. The objective of the present paper is to deepen the investigation of such mean-field stochastic differential equations by studying them in a Brownian motion framework. By constructing a coupling, log-Harnack inequality and Harnack inequality with dimension-free are established for such mean-field stochastic differential equations.
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