This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

Now back in print by the AMS, this is a significantly revised edition of a book originally
published in 1987 by Academic Press. This book gives the reader an introduction to the …

Under integrability conditions on distribution dependent coefficients, existence and
uniqueness are proved for distribution dependent SDEs with non-degenerate noise. When …

In this paper we study Lipschitz regularity of elliptic PDEs on geometric graphs, constructed
from random data points. The data points are sampled from a distribution supported on a …

This paper considers multidimensional jump type stochastic differential equations with super
linear and non-Lipschitz coefficients. After establishing a sufficient condition for …

We derive explicitly the coupling property for the transition semigroup of a Lévy process and
gradient estimates for the associated semigroup of transition operators. This is based on the …

We consider general Markov processes with absorption and provide criteria ensuring the
exponential convergence in total variation of the distribution of the process conditioned not …

We present a novel approach of coupling two multi-dimensional and non-degenerate Itô
processes (X_t) and (Y_t) which follow dynamics with different drifts. Our coupling is sticky in …

This work focuses on a class of regime-switching jump diffusion processes, in which the
switching component has countably infinite many states or regimes. The existence and …

Under Lyapunov and monotone conditions, the exponential ergodicity in the induced
Wasserstein quasi-distance is proved for a class of non-dissipative McKean-Vlasov SDEs …