Knani, H

In this paper, we generalize to Gaussian Volterra processes the existence and uniqueness of solutions for a class of non linear backward stochastic differential equations (BSDE) and we establish the relation between the non linear BSDE and the partial differential equation (PDE). A comparison theorem for the solution of the BSDE is proved and the c...

koike, yuta

This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the wei...

Clarke De La Cerda, Jorge Olivera, Christian Tudor, Ciprian

We analyze the transport equation driven by a zero quadratic variation process. Using the stochastic calculus via regularization and the Malliavin calculus techniques, we prove the existence, uniqueness and absolute continuity of the law of the solution. As an example, we discuss the case when the noise is a Hermite process.

Bellingeri, Carlo

We use the recent theory of regularity structures to develop an It\^o formula for $u$, the stochastic heat equation with space-time white noise in one space dimension with periodic boundary conditions. In particular for any smooth enough function $\phi$ we can express the random distribution $(\partial_t-\partial_{xx})\phi(u)$ and the random field ...

Coutin, L. Decreusefond, Laurent

We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus of the solution of the Stein's equation. As an application, we can evaluate the rate of convergence towards the local time at 0 of the Brownian motion.

Knani, H Dozzi, M

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaus-sian Volterra processes are given. These processes include the multifractional brownian motion and the mul-tifractional Ornstein-Uhlenbeck process. By an Itô formula, proven in the context of Malliavin calculus, the BSDE is associated to a line...

Decreusefond, Laurent Halconruy, Hélène

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which s...

Slaoui, Meryem Tudor, Ciprian A.

We consider the Wiener integral with respect to a $d$-parameter Hermite process with Hurst multi-index ${\bf H}= (H_{1},\ldots, H_{d}) \in \left( \frac{1}{2}, 1\right) ^{d}$ and we analyze the limit behavior in distribution of this object when the components of ${\bf H}$ tend to $1$ and/or $\frac{1}{2}$. As examples, we focus on the solution to the...

Kim, Yoon Tae Park, Hyun Suk
Published in
Journal of the Korean Statistical Society

This paper is concerned with the exact rate of convergence of the distribution of the sequence {Fn}, where each Fn is a functional of an infinite-dimensional Gaussian field. Nourdin and Peccati (2015) obtain a quantitative bound to complement the fourth moment theorem, by which a sequence in a fixed Wiener chaos converges in law to normal distribut...

Coutin, Laure Pontier, Monique

Let X be a continuous $d$-dimensional diffusion process and M the running supremum of the first component. We show that, for any t>0, the law of the (d+1) random vector (M_t,X_t) admits a density with respect to the Lebesgue measure using Malliavin's calculus. In case $d=1$ we prove the regularity of this density. Abstract Let X be a continuous d-d...