Mathematics Scholarly Works: Recent submissions

Now showing items 141-160 of 283

    • Markov Field Property of Stochastic Differential Equations 

      Darses, Sebastien; Nourdin, Ivan; Nualart, David (Institute of Mathematical Statistics (IMS), 1995-03-01)
      The purpose of this paper is to prove a characterization of the conditional independence of two independent random variables given a particular functional of them, in terms of a factorization property. As an application ...

    • Points of Positive Density for Smooth Functionals 

      Chaleyat-Maurel, Mireille; Nualart, David (Institute of Mathematical Statistics (IMS), 1998-12-03)
      In this paper we show that the set of points where the density of a Wiener functional is strictly positive is an open connected set, assuming some regularity conditions.

    • Stochastic evolution equations with random generators 

      Leon, Jorge A.; Nualart, David (Institute of Mathematical Statistics (IMS), 1998-05-01)
      We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is supposed to be random ...

    • Evolution equation of a stochastic semigroup with white-noise drift 

      Nualart, David; Viens, Frederi (Institute of Mathematical Statistics (IMS), 2000-09-20)
      We study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup whose kernel p(s,t,y,x) is Brownian in s and t.The kernel p is supposed to be measurable ...

    • Stochastic Calculus with Respect to Gaussian Processes 

      Alos, Elisa; Mazet, Olivier; Nualart, David (Institute of Mathematical Statistics, 2001-12-05)
      In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bt=∫t0K(t,s)dWs, where W is a Wiener process and K(t,s) is a square integrable kernel, using the techniques of the stochastic ...

    • Smoothness of the law of the supremum of the fractional Brownian motion 

      Zadi, Noureddine Lanjri; Nualart, David (Institute of Mathematical Statistics, 2003-07-25)
      This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter H∈(0,1) has an infinitely differentiable density on (0,∞). The proof of this result is based on the techniques of the ...

    • Probabilistic models for vortex filaments based on fractional Brownian motion 

      Nualart, David; Rovira, Carles; Tindel, Samy (Institute of Mathematical Statistics (IMS), 2003-11-01)
      We consider a vortex structure based on a three-dimensional fractional Brownian motion with Hurst parameter H>12. We show that the energy H\vspace*{-1pt} has moments of any order under suitable conditions. When H∈(12,13) ...

    • Renormalized self-intersection local time for fractional Brownian motion 

      Hu, Yaozhong; Nualart, David (Institute of Mathematical Statistics, 2005-05-06)

    • Central limit theorems for sequences of multiple stochastic integrals 

      Nualart, David; Peccati, Giovanni (Institute of Mathematical Statistics (IMS), 2005-01-01)
      We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study ...

    • Notes on the two-dimensional fractional Brownian motion 

      Baudoin, Fabrice; Nualart, David (Institute of Mathematical Statistics, 2006-02-17)
      We study the two-dimensional fractional Brownian motion with Hurst parameter H>½. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation ...

    • Regularity of the density for the stochastic heat equation 

      Mueller, Carl; Nualart, David (Institute of Mathematical Statistics (IMS), 2008-12-18)
      We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear ...

    • Rough path analysis via fractional calculus 

      Hu, Yaozhong; Nualart, David (American Mathematical Society, 2009-11-02)

    • Stochastic integral representation of the L2 modulus of Brownian local time and a central limit theorem 

      Hu, Yaozhong; Nualart, David (Institute of Mathematical Statistics (IMS), 2009-11-09)
      The purpose of this note is to prove a central limit theorem for the L2-modulus of continuity of the Brownian local time obtained in [3], using techniques of stochastic analysis. The main ingredients of the proof are an ...

    • Fractional martingales and characterization of the fractional Brownian motion 

      Hu, Yaozhong; Nualart, David; Song, Jian (Institute of Mathematical Statistics, 2009-11-19)
      In this paper we introduce the notion of fractional martingale as the fractional derivative of order α of a continuous local martingale, where α∈(−½, ½), and we show that it has a nonzero finite variation of order 2/(1+2α), ...

    • Central limit theorem for the third moment in space of the Brownian local time increments 

      Hu, Yaozhong; Nualart, David (Institute of Mathematical Statistics (IMS), 2010-09-14)
      The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic ...

    • Limit theorems for nonlinear functionals of Volterra processes via white noise analysis 

      Darses, Sebastien; Nourdin, Ivan; Nualart, David (Bernoulli Society for Mathematical Statistics and Probability, 2010-11-10)
      By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the ...

    • Central and non-central limit theorems for weighted power variations of fractional Brownian motion 

      Nourdin, Ivan; Nualart, David; Tudor, Ciprian A. (Annals of the Institute Henri Poincaré, 2010-10-01)
      n this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional Brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central ...

    • Feynman-Kac formula for the heat equation driven by fractional white noise 

      Hu, Yaozhong; Nualart, David; Song, Jian (Institute of Mathematical Statistics, 2011-02-01)
      We establish a version of the Feynman–Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process ...

    • A construction of the rough path above fractional Brownian motion using Volterra’s representation 

      Nualart, David; Tindel, Samy (Institute of Mathematical Statistics, 2011-09-01)
      This note is devoted to construct a rough path above a multidimensional fractional Brownian motion B with any Hurst parameter H∈(0, 1), by means of its representation as a Volterra Gaussian process. This approach yields ...

    • Malliavin calculus for backward stochastic differential equations and applications to numerical solutions 

      Hu, Yaozhong; Nualart, David; Song, Xiaoming (Institute of Mathematical Statistics, 2011-04-01)
      In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The ...