The capitalization-weighted cumulative variation i=1^d0^⋅i(t)\,d⟨\logi⟩(t) in an equity
market consisting of a fixed number d of assets with capitalization weights i(⋅), is an …

We study a class of R^d-valued continuous strong Markov processes that are generated,
only locally, by an ultra-parabolic operator with coefficients that are regular wrt the intrinsic …

We consider a diffusion process under a local weak Hörmander condition on the
coefficients. We find Gaussian estimates for the density in short time and exponential lower …

We study a system of n differential equations, each in dimension d. Only the first equation is
forced by a Brownian motion and the dependence structure is such that, under a local weak …

We study the wellposedness of the master equation for a second-order mean field games
with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by …

We study lower and upper bounds for the probability that a diffusion process in R^n remains
in a tube around a deterministic skeleton path up to a fixed time. The diffusion coefficients …

We study lower and upper bounds for the density of a diffusion process in Rn in a small (but
not asymptotic) time, say δ. We assume that the diffusion coefficients σ1,..., σd may …

One of the purposes of this thesis is to use Malliavin calculus and Stochastic Taylor
expansions to study the densities of interacting systems of stochastic differential equations …

We study lower and upper bounds for the density of a diffusion process in ${\mathbb {R}}^ n
$ in a small (but not asymptotic) time, say $\delta $. We assume that the diffusion coefficients …