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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.
List of contents
Stochastic Analysis and Random Fields.- Gaussian random fields on manifolds.- Higher order expansions for the overlap of the SK model.- Poissonian exponential functionalsq-seriesq-integrals, and the moment problem for log-normal distributions.- A Littlewood-Paley type inequality on the path space.- Condition numbers and extrema of random fields.- Second-order hyperbolic S.P.D.E.'s driven by boundary noises.- Stochastic heat and Burgers equations and the intermittence of turbulence.- Averaging of a parabolic partial differential equation with random evolution.- Random currents and probabilistic models of vortex filaments.- Stochastic resonance: a comparative study of two-state models.- Sample Hölder continuity of stochastic processes and majorizing measures.- Hypoelliptic diffusions and cyclic cohomology.- Isovectors for the Hamilton-Jacobi-Bellman equation,formal stochastic differentials and first integrals in Euclidean quantum mechanics.- Stochastic Methods in Financial Models.- Superhedging strategies and balayage in discrete time.- Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes.- Stochastic volatility and correction to the heat equation.- Bayesian estimate of default probabilities via MCMC with delayed rejection.- Optimal portfolio in a multiple-priors model.- Indifference pricing with exponential utility.
Summary
This volume contains twenty refereed research or review papers presented at the 4th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità ) in Ascona, Switzerland, from May 19 to 24, 2002. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering.
The book will be a valuable resource for both researchers in stochastic analysis and professionals interested in stochastic methods in finance and insurance.
