In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a Hölder continuous function with parameter greater that 1/2 via the Young integration setting. Then some estimates of the solution are obtained, which allow to show that the solution of a delay differential equation driven by a fractional Brownian motion (fBm) with Hurst...

We consider a solution xt to a generic Markovian jump diffusion and show that for any t0 > 0 the law of xt0 has a C ∞ density with respect to Lebesgue measure under a uniform version of Hörmander’s conditions. Unlike previous results in the area the result covers a class of infinite activity jump processes. The result is accompolished by using carefully crafted refinements to the classical argu...

Overview. In a seminal paper of 2005, Nualart and Peccati [40] discovered a surprising central limit theorem (called the “Fourth Moment Theorem” in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution to the standard normal law is equivalent to convergence of just the fourth moment. Shortly afterwards, Peccati and Tudor [46] g...

We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that may be anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore, if the inve...

We propose a novel method to solve chemical diffusion master equation of birth and death type. This is an infinite system Fokker-Planck equations where the different components are coupled by reaction dynamics similar in form equation. was proposed [4] for modelling probabilistic evolution kinetics associated with spatial individual particles. Using some basic tools ideas from dimensional Gauss...

In this paper we state and prove a central limit theorem for the finite-dimensional laws of the quadratic variations process of certain fractional Brownian sheets. The main tool of this article is a method developed by Nourdin and Nualart in [17] based on the Malliavin calculus.