35 citations · 132 across the 28 of their papers we have counts for
22 papers · 1 filter
Ergodic approximation for the invariant distribution: An abstract framework for law-dependent dynamics
Aurélien Alfonsi, Vlad Bally, Lucia Caramellino +1
This paper studies the approximation of invariant distributions for a broad class of law-dependent dynamics, including McKean-Vlasov stochastic differential equations and Boltzmann…
Convergence in Total Variation for nonlinear functionals of random hyperspherical harmonics
Lucia Caramellino, Giacomo Giorgio, Maurizia Rossi
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit -dimensional sphere (). We study the convergence in Total Variation distance for their no…
Regularization lemmas and convergence in total variation
Vlad Bally, Lucia Caramellino, Guillaume Poly
We provide a simple abstract formalism of integration by parts under which we obtain some regularization lemmas. These lemmas apply to any sequence of random variables whic…
Transfer of regularity for Markov semigroups
Vlad Bally, Lucia Caramellino
We study the regularity of a Markov semigroup , that is, when for a suitable smooth function . This is done by transferring the regula…
Convergence rate of Markov chains and hybrid numerical schemes to jump-diffusions with application to the Bates model
Maya Briani, Lucia Caramellino, Giulia Terenzi
We study the rate of weak convergence of Markov chains to diffusion processes under suitable but quite general assumptions. We give an example in the financial framework, applying…
Non universality for the variance of the number of real roots of random trigonometric polynomials
Vlad Bally, Lucia Caramellino, Guillaume Poly
In this article, we consider the following family of random trigonometric polynomials for a given sequence of i.i.d. random…
Total variation distance between stochastic polynomials and invariance principles
Vlad Bally, Lucia Caramellino
The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynom…
Diffusions under a local strong Hörmander condition. Part II: tube estimates
Vlad Bally, Lucia Caramellino, Paolo Pigato
We study lower and upper bounds for the probability that a diffusion process in remains in a tube around a skeleton path up to a fixed time. We assume that the diffu…
Diffusions under a local strong Hörmander condition. Part I: density estimates
Vlad Bally, Lucia Caramellino, Paolo Pigato
We study lower and upper bounds for the density of a diffusion process in in a small (but not asymptotic) time, say . We assume that the diffusion coefficients…
An Invariance Principle for Stochastic Series II. Non Gaussian Limits
Vlad Bally, Lucia Caramellino
We study the convergence in total variation distance for series of the form whe…
Convergence in distribution norms in the CLT for non identical distributed random variables
Vlad Bally, Lucia Caramellino, Guillaume Poly
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\fr…
An invariance principle for stochastic series I. Gaussian limits
Vlad Bally, Lucia Caramellino
We study invariance principles and convergence to a Gaussian limit for stochastic series of the form $S(c,Z)=\sum_{m=1}^{\infty }\sum_{α_{1}<...<α_{m}}c(α_{1},...,α_{m})\prod_{i=1}…
On Sharp Large Deviations for the bridge of a general Diffusion
Paolo Baldi, Lucia Caramellino, Maurizia Rossi
We provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a -dimensional general diffusion process , as the conditioning time ten…
Convergence and regularity of probability laws by using an interpolation method
V. Bally, L. Caramellino
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Hölder continuous c…
Asymptotic development for the CLT in total variation distance
Vlad Bally, Lucia Caramellino
The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the…
Large Deviation asymptotics for the exit from a domain of the bridge of a general Diffusion
Paolo Baldi, Lucia Caramellino, Maurizia Rossi
We provide Large Deviation estimates for the bridge of a -dimensional general diffusion process as the conditioning time tends to and apply these results to the evaluation o…
On the distance between probability density functions
Vlad Bally, Lucia Caramellino
We give estimates of the distance between the densities of the laws of two functionals and on the Wiener space in terms of the Malliavin-Sobolev norm of We actually…
Regularity of probability laws by using an interpolation method
Vlad Bally, Lucia Caramellino
We study the problem of the existence and regularity of a probability density in an abstract framework based on a "balancing" with approximating absolutely continuous laws. Typical…
Tubes estimates for diffusion processes under a local Hörmander condition of order one
Vlad Bally, Lucia Caramellino
We consider a diffusion process and a skeleton curve and we give a lower bound for . This result is obtained under the…
Positivity and lower bounds for the density of Wiener functionals
V. Bally, L. Caramellino
We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion of strict positivity of the density. We also give lower…
Riesz transform and integration by parts formulas for random variables
Vlad Bally, Lucia Caramellino
We use integration by parts formulas to give estimates for the norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of fu…
Large deviation estimates of the crossing probability for pinned Gaussian processes
L. Caramellino, B. Pacchiarotti
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in fixed points at fixed past instants. In particular, functional large…