Seminar on Stochastic Analysis, Random Fields and Applications

1. Front Matter

   Pages i-x

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2. Propagation of Chaos — The Inverse Problem

   1. Propagation of Chaos — The Inverse Problem

      • Robert Aebi

      Pages 1-25

3. A Remark on Stochastic Dynamics on the Infinite-Dimensional Torus

   1. A Remark on Stochastic Dynamics on the Infinite-Dimensional Torus

      • S. Albeverio, Yu. G. Kondratiev, M. Röckner

      Pages 27-35

4. Diffusion-Approximation for the Advection-Diffusion of a Passive Scalar by a Space-Time Gaussian Velocity Field

   1. Diffusion-Approximation for the Advection-Diffusion of a Passive Scalar by a Space-Time Gaussian Velocity Field

      • René A. Carmona, Jean Pierre Fouque

      Pages 37-49

5. A New Space of White Noise Distributions and Applications to SPDE’s

   1. A New Space of White Noise Distributions and Applications to Spde’s

      • René A. Carmona, J. A. Yan

      Pages 51-66

6. Dissipativity of Three-Dimensional Stochastic Navier-Stokes Equation

   1. Dissipativity of Three-Dimensional Stochastic Navier-Stokes Equation

      • Hans Crauel, Franco Flandoli

      Pages 67-76

7. Bernstein Diffusions and Euclidean Quantum Field Theory

   1. Bernstein Diffusions and Euclidean Quantum Field Theory

      • A. B. Cruzeiro, Z. Haba, J. C. Zambrini

      Pages 77-97

8. A Fubini Theorem for Generalized Stratonovich Integrals

   1. A Fubini Theorem for Generalized Stratonovich Integrals

      • Rosario Delgado, Marta Sanz-Solé

      Pages 99-110

9. Large Deviations via Parameter Dependent Change of Measure, and an Application to the Lower Tail of Gaussian Processes

   1. Large Deviations via Parameter Dependent Change of Measure, and an Application to the Lower Tail of Gaussian Processes

      • Amir Dembo, Ofer Zeitouni

      Pages 111-121

10. An Equation Modelling Transport of a Substance in a Stochastic Medium

    1. An Equation Modelling Transport of a Substance in a Stochastic Medium

       • Jon Gjerde, Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang

       Pages 123-134

11. Stochastic Representation of Unitary Quantum Evolution

    1. Stochastic Representation of Unitary Quantum Evolution

       • Z. Haba

       Pages 135-149

12. Critical Dimensions for the Existence of Self-Intersection Local Times of the Brownian Sheet in ℝ d

    1. Critical Dimensions for the Existence of Self-Intersection Local Times of the Brownian Sheet in ℝ^d

       • Peter Imkeller, Ferenc Weisz

       Pages 151-168

13. Density Estimates for Stochastic Partial Differential Equations

    1. Density Estimates for Stochastic Partial Differential Equations

       • Rémi Léandre, Francesco Russo

       Pages 169-186

14. Density estimates for stochastic partial differential equations

    1. Almost Sure Convergence of Stochastic Differential Equations of Jump-Diffusion Type

       • C. W. Li

       Pages 187-197

15. Applications and Foundations of Quasi Sure Analysis

    1. Applications and Foundations of Quasi Sure Analysis

       • Paul Malliavin

       Pages 199-203

16. A Duality Formula on the Poisson Space and Some Applications

    1. A Duality Formula on the Poisson Space and Some Applications

       • David Nualart, Josep Vives

       Pages 205-213

17. Generalized Functions and Stochastic Processes

    1. Generalized Functions and Stochastic Processes

       • Michael Oberguggenberger

       Pages 215-229

18. On the Geometry Defined by Dirichlet Forms

    1. On the Geometry Defined by Dirichlet Forms

       • Karl-Theodor Sturm

       Pages 231-242

19. Random Brownian Scaling and Some Absolute Continuity Relationships

    1. Random Brownian Scaling and Some Absolute Continuity Relationships

       • Marc Yor

       Pages 243-252

20. Recent Progress in the Hypercontractive Semigroups

    1. Recent Progress in the Hypercontractive Semigroups

       • Boguslaw Zegarlinski

       Pages 253-262

Pure and applied stochastic analysis and random fields form the subject of this book. The collection of articles on these topics represent the state of the art of the research in the field, with particular attention being devoted to stochastic models in finance. Some are review articles, others are original papers; taken together, they will apprise the reader of much of the current activity in the area.

• Black-Scholes
• Dirichlet form
• Gaussian process
• Martingale
• Stochastic processes
• local martingale
• local time
• stochastic process

• Institut für Mathematik, Abteilung Angewandte Mathematik, Universität Zürich-Irchel, Zürich, Switzerland

  Erwin Bolthausen

• Département de Mathématiques, Université de Nancy 1, Vandoeuvre-Les-Nancy Cedex, France

  Marco Dozzi

• Département de Mathématiques Institut Galilée, Université Paris-Nord, Villetaneuse, France

  Francesco Russo

• BIBOS, Universität Bielefeld, Bielefeld 1, Germany

  Francesco Russo

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