Seminar on Stochastic Analysis, Random Fields and Applications IV

1. Front Matter

   Pages i-xii

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2. Stochastic Analysis and Random Fields

   1. Front Matter

      Pages 1-1

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   2. Gaussian Random Fields on Manifolds

      • Robert J. Adler

      Pages 3-19

   3. Higher Order Expansions for the Overlap of the SK Model

      • Xavier Bardina, David Márquez-Carreras, Carles Rovira, Samy Tindel

      Pages 21-43

   4. Poissonian Exponential Functionals, q-Series, q-Integrals, and the Moment Problem for log-Normal Distributions

      • Jean Bertoin, Philippe Biane, Marc Yor

      Pages 45-56

   5. A Littlewood-Paley Type Inequality on the Path Space

      • Ana Bela Cruzeiro, Xicheng Zhang

      Pages 57-67

   6. Condition Numbers and Extrema of Random Fields

      • J. A. Cuesta-Albertos, Mario Wschebor

      Pages 69-82

   7. Second-Order Hyperbolic S.P.D.E.’s Driven by Boundary Noises

      • Robert C. Dalang, Olivier Lévêque

      Pages 83-93

   8. Stochastic Heat and Burgers Equations and the Intermittence of Turbulence

      • Ian M. Davies, Aubrey Truman, Huaizhong Zhao

      Pages 95-110

   9. Averaging of a Parabolic Partial Differential Equation with Random Evolution

      • Mamadou Abdoul Diop, Etienne Pardoux

      Pages 111-128

   10. Random Currents and Probabilistic Models of Vortex Filaments

       • Franco Flandoli, Massimiliano Gubinelli

       Pages 129-139

   11. Stochastic Resonance: A Comparative Study of Two-State Models

       • Peter Imkeller, Ilya Pavlyukevich

       Pages 141-154

   12. Sample Hölder Continuity of Stochastic Process and Majorizing Measures

       • Stanisław Kwapień, Jan Rosiński

       Pages 155-163

   13. Hypoelliptic Diffusions and Cyclic Cohomology

       • Rémi Léandre

       Pages 165-185

   14. Isovectors for the Hamilton-Jacobi-Bellman Equation, Formal Stochastic Differentials and First Integrals in Euclidean Quantum Mechanics

       • Paul Lescot, Jean-Claude Zambrini

       Pages 187-202

3. Stochastic Methods in Financial Models

   1. Front Matter

      Pages 203-203

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   2. Superhedging Strategies and Balayage in Discrete Time

      • Simone Deparis, Claude Martini

      Pages 205-219

   3. Generalized Hyperbolic and Inverse Gaussian Distributions: Limiting Cases and Approximation of Processes

      • Ernst Eberlein, Ernst August v. Hammerstein

      Pages 221-264

   4. Stochastic Volatility and Correction to the Heat Equation

      • Jean-Pierre Fouque, George Papanicolaou, Ronnie Sircar

      Pages 265-274

   5. Bayesian Estimate of Default Probabilities via MCMC with Delayed Rejection

      • Antonietta Mira, Paolo Tenconi

      Pages 275-289

This volume contains the Proceedings of the Fourth Seminar on Stochastic Analy­ sis, Random Fields and Applications, which took place at the Centro Stefano Fran­ scini (Monte Verita) in Ascona (Ticino), Switzerland, from May 20 to 24, 2002. The first three editions of this conference occured in 1993, 1996 and 1999. The Seminar covered several topics: fundamental aspects of stochastic analysis, such as stochastic partial differential equations and random fields, and applications to current active fields such as probabilistic methods in fluid dynamics, biomathe­ matics, and financial modeling. As in the previous editions, this last topic was the subject of the Fourth Minisymposium on Stochastic Methods in Financial Models. These proceedings aim to present key aspects of these topics to a larger audience. All papers in this volume have been refereed. A major topic within Stochastic Analysis is the area of random fields which includes as particular cases, Gaussian random fields, stochastic partial differential equations (s. p. d. e. 's) and stochastic differential equations with values in Banach spaces. In this framework, interesting new developments were presented in the theory of Gaussian random fields on manifolds with applications to astrophysics and neurosciences. Moreover, with the aim of modeling certain very irregular phe­ nomena, a theory of s. p. d. e. 's driven by noises concentrated on hyperplanes was presented.

• Fractals
• Gaussian distribution
• Normal distribution
• Random fields
• Stochastic Analysis
• Stochastic processes
• calculus
• path space
• stochastic process

• Institut de Mathématiques, Ecole Polytechnique Fédérale, Lausanne, Switzerland

  Robert C. Dalang

• Institut Elie Cartan, Université Henri Poincaré, Vandoeuvre-lès-Nancy Cedex, France

  Marco Dozzi

• Département de Mathématiques, Institut Galilée, Villetaneuse, France

  Francesco Russo

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