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Malliavin Calculus and Stochastic Analysis

A Festschrift in Honor of David Nualart

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Frederi Viens

    1. , Department of Statistics, Purdue University, West Lafayette, USA

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  2. Jin Feng

    1. , Department of Mathematics, University of Kansas, Lawrence, USA

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  3. Yaozhong Hu

    1. Dept. Mathematics, University of Kansas, Lawrence, USA

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  4. Eulalia Nualart 

    1. , Department of Economics and Business, University Pompeu Fabra, Barcelona, Spain

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  • Its scope spans most uses of the Malliavin calculus
  • Gathers most of the major players in Malliavin calculus and stochastic analysis worldwide
  • Honors Professor David Nualart, who is considered by many as the world leader in propagating the Malliavin calculus
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 34)

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Table of contents (25 papers)

  1. Front Matter

    Pages i-xi
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  2. Malliavin Calculus and Wiener Space Theory

    1. Front Matter

      Pages 1-1
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    2. An Application of Gaussian Measures to Functional Analysis

      • Daniel W. Stroock
      Pages 3-8

    3. Stochastic Taylor Formulas and Riemannian Geometry

      • Mark A. Pinsky
      Pages 9-23

    4. Local Invertibility of Adapted Shifts on Wiener Space and Related Topics

      • Rémi Lassalle, A. S. Üstünel
      Pages 25-76

    5. Dilation Vector Field on Wiener Space

      • Hélène Airault
      Pages 77-94

    6. The Calculus of Differentials for the Weak Stratonovich Integral

      • Jason Swanson
      Pages 95-111

  3. Stochastic Differential Equations

    1. Front Matter

      Pages 113-113
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    2. Large Deviations for Hilbert-Space-Valued Wiener Processes: A Sequence Space Approach

      • Andreas Andresen, Peter Imkeller, Nicolas Perkowski
      Pages 115-138

    3. Stationary Distributions for Jump Processes with Inert Drift

      • K. Burdzy, T. Kulczycki, R. L. Schilling
      Pages 139-172

    4. An Ornstein-Uhlenbeck-Type Process Which Satisfies Sufficient Conditions for a Simulation-Based Filtering Procedure

      • Arturo Kohatsu-Higa, Kazuhiro Yasuda
      Pages 173-193

    5. Escape Probability for Stochastic Dynamical Systems with Jumps

      • Huijie Qiao, Xingye Kan, Jinqiao Duan
      Pages 195-216

  4. Stochastic Partial Differential Equations

    1. Front Matter

      Pages 217-217
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    2. On the Stochastic Navier–Stokes Equation Driven by Stationary White Noise

      • Chia Ying Lee, Boris Rozovskii
      Pages 219-249

    3. Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1

      • Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan Shiu
      Pages 251-279

    4. Generalized Stochastic Heat Equations

      • David Márquez-Carreras
      Pages 281-297

    5. Gaussian Upper Density Estimates for Spatially Homogeneous SPDEs

      • Lluís Quer-Sardanyons
      Pages 299-314

    6. Stationarity of the Solution for the Semilinear Stochastic Integral Equation on the Whole Real Line

      • Bijan Z. Zangeneh
      Pages 315-331

  5. Fractional Brownian Models

    1. Front Matter

      Pages 333-333
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    2. A Strong Approximation of Subfractional Brownian Motion by Means of Transport Processes

      • Johanna Garzón, Luis G. Gorostiza, Jorge A. León
      Pages 335-360
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Keywords

About this book

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.

Editors and Affiliations

  • , Department of Statistics, Purdue University, West Lafayette, USA

    Frederi Viens

  • , Department of Mathematics, University of Kansas, Lawrence, USA

    Jin Feng

  • Dept. Mathematics, University of Kansas, Lawrence, USA

    Yaozhong Hu

  • , Department of Economics and Business, University Pompeu Fabra, Barcelona, Spain

    Eulalia Nualart 

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