Integration with respect to local time and Ito's formula for smooth nondegenerate martingales (2008)
Bardina, Xavier, Rovira, Carles
We show an It\^ o's formula for nondegenerate Brownian martingales $X_t=\int_0^t u_s dW_s$ and functions $F(x,t)$ with locally integrable derivatives in $t$ and $x$. We prove that one can express the...
A model of continuous time polymer on the lattice (2008)
Marquez-Carreras, David, Rovira, Carles, Tindel, Samy
In this article, we try to give a rather complete picture of the behavior of the free energy for a model of directed polymer in a random environment, in which the polymer is a simple symmetric random...
On It\^{o}'s formula for elliptic diffusion processes (2007)
Bardina, Xavier, Rovira, Carles
Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83--109] prove an extension of It\^{o}'s formula for $F(X_t,t)$, where $F(x,t)$ has a locally square-integrable derivative in $x$ that satisfies...
Asymptotic behavior of the magnetization for the perceptron model (2007)
Marquez-Carreras, David, Rovira, Carles, Tindel, Samy
In this paper, we show that, in case of a perceptron model for which the number of outputs is a small proportion of the size of the system, the limiting behavior of the magnetization of a given spin,...
Asymptotic behavior of the magnetization for the perceptron model (2007)
Marquez-Carreras, David, Rovira, Carles, Tindel, Samy
In this paper, we show that, in case of a perceptron model for which the number of outputs is a small proportion of the size of the system, the limiting behavior of the magnetization of a given spin,...
A diluted version of the perceptron model (2006)
Marquez-Carreras, David, Rovira, Carles, Tindel, Samy
This note is concerned with a diluted version of the perceptron model. We establish a replica symmetric formula at high temperature, which is achieved by studying the asymptotic behavior of a given...
Ferrante, Marco, Rovira, Carles
We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>½. We prove an existence and uniqueness result for this...
On the Brownian directed polymer in a Gaussian random environment (2004)
In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are...
Probabilistic models for vortex filaments based on fractional Brownian motion (2003)
Nualart, David, Rovira, Carles, Tindel, Samy
We consider a vortex structure based on a three-dimensional fractional Brownian motion with Hurst parameter $H>\frac{1}{2}.$ We show that the energy $\mathbb{H}$\vspace*{-1pt} has moments of any...
Large deviations for stochastic Volterra equations (2000)
Nualart, David, Rovira, Carles
This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.