Related papers: The central limit theorem for stochastic Volterra …

This is a note on some results of the central limit theorem for deterministic dynamical systems. First, we give the central limit theorem for martingales, which is a main tool. Then we give the main results on the central limit theorem in…

In this paper we obtain a rate of convergence in the central limit theorem for high order weighted Hermite variations of the fractional Brownian motion. The proof is based on the techniques of Malliavin calculus and the quantitative stable…

In this paper, we study linear backward stochastic differential equations driven by a class of centered Gaussian non-martingales, including fractional Brownian motion with Hurst parameter $H\in (0,1)\setminus \{\frac12\}$. We show that, for…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…

Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…

We give a new estimate on Stieltjes integrals of H\"older continuous functions and use it to prove an existence-uniqueness theorem for solutions of ordinary differential equations with H\"older continuous forcing. We construct stochastic…

In this paper we show a central limit theorem for Lebesgue integrals of stationary $BL(\theta)$-dependent random fields as the integration domain grows in Van Hove-sense. Our method is to use the (known) analogue result for discrete sums.…

We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by…

A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.

We investigate the properties of the solutions of scaled Volterra equations (i.e. with an affine mean-reverting drift) in terms of stationarity at both a finite horizon and on the long run. In particular we prove that such an equation never…

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…

We obtain limit theorems for a class of nonlinear discrete-time processes $X(n)$ called the $k$-th order Volterra processes of order $k$. These are moving average $k$-th order polynomial forms: \[…

We study first order linear partial differential equations that appear, for example, in the analysis of dimishing urn models with the help of the method of characteristics and formulate sufficient conditions for a central limit theorem.

In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H >…

We consider a stochastic Volterra integral equation with regular path-dependent coefficients and a Brownian motion as integrator in a multidimensional setting. Under an imposed absolute continuity condition, the unique solution is a…

We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear…

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

This paper deals with the well posedness of an integrodifferential equation that describes a vortex filament associated to a 3D turbulent fluid flow. This equation is driven by a fractional Brownian motion of Hurst parameter H>1/2. We prove…

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…