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;

Propagation of chaos — the inverse problem.- A remark on stachastic dynamics on the infinite-dimensional torus.- Diffusion-approximation for the advection-diffusion of a passive scalar by a space-time Gaussian velocity field.- A new space of white noise distributions and applications to SPDE’s.- Dissipativity of three-dimensional stochastic Navier-Stokes equation.- Bernstein diffusions and Euclidean quantum field theory.- A Fubini theorem for generalized Stratonovich integrals.- Large deviations via parameter dependent change of measure, and an application to the lower tail of Gaussian processes.- An equation modelling transport of a substance in a stochastic medium.- Stochastic representation of unitary quantum evolution.- Critical dimensions for the existence of self-intersection local times of the Brownian sheet in ?d.- Density estimates for stochastic partial differential equations.- Almost sure convergence of stochastic differential equations of jump-diffusion type.- Applications and foundations of quasi sure analysis.- A duality formula on the Poisson space and some applications.- Generalized functions and stochastic processes.- On the geometry defined by Dirichlet forms.- Random Brownian scaling and some absolute continuity relationships.- Recent progress in the hypercontractive semigroups.- Financial models.- Alternative estimators of a diffusion model of the term structure of interest rates. A Monte Carlo comparison.- Backward stochastic differential equations. Option hedging under additional cost.- Componentwise and vector stochastic integration with respect to certain multi-dimensional continuous local martingales.- Stock price returns and the Joseph effect: A fractional version of the Black-Scholes model.- Critical price for an American option nearmaturity.- Hedging of options under discrete observation on assets with stochastic volatility.- Convergence of option values under incompleteness.- Portfolio selection with transaction costs.

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