A nonlinear Markov evolution is a dynamical system generated by a measure-valued
ordinary differential equation with the specific feature of preserving positivity. This feature …

This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

In this paper, we investigate the mean field games with $ K $ classes of agents who are
weakly coupled via the empirical measure. The underlying dynamics of the representative …

This is an advanced text on ordinary differential equations (ODEs) in Banach and more
general locally convex spaces, most notably ODEs on measures and various function …

We consider the spatially inhomogeneous Landau equation with soft potentials. First, we
establish the short-time existence of solutions, assuming the initial data has sufficient decay …

This article investigates several properties related to densities of solutions (X_t)_t∈0,1 to
differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4 …

In this paper, we investigate the mean field games of N agents who are weakly coupled via
the empirical measures. The underlying dynamics of the representative agent is assumed to …

We give lower bounds for the density p T (x, y) of the law of X t, the solution of dX t= σ (X t) dB
t+ b (X t) dt, X 0= x, under the following local ellipticity hypothesis: there exists a deterministic …

Ito's construction of Markovian solutions to stochastic equations driven by a Lévy noise is
extended to nonlinear distribution dependent integrands aiming at the effective construction …

In this paper, we establish lower and upper Gaussian bounds for the probability density of
the mild solution to the non-linear stochastic heat equation in any space dimension. The …