Ebook: Seminar on Stochastic Analysis, Random Fields and Applications IV: Centro Stefano Franscini, Ascona, May 2002

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.

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Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Gaussian Random Fields on Manifolds....Pages 3-19
Higher Order Expansions for the Overlap of the SK Model....Pages 21-43
Poissonian Exponential Functionals, q-Series, q-Integrals, and the Moment Problem for log-Normal Distributions....Pages 45-56
A Littlewood-Paley Type Inequality on the Path Space....Pages 57-67
Condition Numbers and Extrema of Random Fields....Pages 69-82
Second-Order Hyperbolic S.P.D.E.’s Driven by Boundary Noises....Pages 83-93
Stochastic Heat and Burgers Equations and the Intermittence of Turbulence....Pages 95-110
Averaging of a Parabolic Partial Differential Equation with Random Evolution....Pages 111-128
Random Currents and Probabilistic Models of Vortex Filaments....Pages 129-139
Stochastic Resonance: A Comparative Study of Two-State Models....Pages 141-154
Sample H?lder Continuity of Stochastic Process and Majorizing Measures....Pages 155-163
Hypoelliptic Diffusions and Cyclic Cohomology....Pages 165-185
Isovectors for the Hamilton-Jacobi-Bellman Equation, Formal Stochastic Differentials and First Integrals in Euclidean Quantum Mechanics....Pages 187-202
Front Matter....Pages 203-203
Superhedging Strategies and Balayage in Discrete Time....Pages 205-219
Generalized Hyperbolic and Inverse Gaussian Distributions: Limiting Cases and Approximation of Processes....Pages 221-264
Stochastic Volatility and Correction to the Heat Equation....Pages 265-274
Bayesian Estimate of Default Probabilities via MCMC with Delayed Rejection....Pages 275-289
Optimal Portfolio in a Multiple-Priors Model....Pages 291-321
Indifference Pricing with Exponential Utility....Pages 323-328

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Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Gaussian Random Fields on Manifolds....Pages 3-19
Higher Order Expansions for the Overlap of the SK Model....Pages 21-43
Poissonian Exponential Functionals, q-Series, q-Integrals, and the Moment Problem for log-Normal Distributions....Pages 45-56
A Littlewood-Paley Type Inequality on the Path Space....Pages 57-67
Condition Numbers and Extrema of Random Fields....Pages 69-82
Second-Order Hyperbolic S.P.D.E.’s Driven by Boundary Noises....Pages 83-93
Stochastic Heat and Burgers Equations and the Intermittence of Turbulence....Pages 95-110
Averaging of a Parabolic Partial Differential Equation with Random Evolution....Pages 111-128
Random Currents and Probabilistic Models of Vortex Filaments....Pages 129-139
Stochastic Resonance: A Comparative Study of Two-State Models....Pages 141-154
Sample H?lder Continuity of Stochastic Process and Majorizing Measures....Pages 155-163
Hypoelliptic Diffusions and Cyclic Cohomology....Pages 165-185
Isovectors for the Hamilton-Jacobi-Bellman Equation, Formal Stochastic Differentials and First Integrals in Euclidean Quantum Mechanics....Pages 187-202
Front Matter....Pages 203-203
Superhedging Strategies and Balayage in Discrete Time....Pages 205-219
Generalized Hyperbolic and Inverse Gaussian Distributions: Limiting Cases and Approximation of Processes....Pages 221-264
Stochastic Volatility and Correction to the Heat Equation....Pages 265-274
Bayesian Estimate of Default Probabilities via MCMC with Delayed Rejection....Pages 275-289
Optimal Portfolio in a Multiple-Priors Model....Pages 291-321
Indifference Pricing with Exponential Utility....Pages 323-328
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