Stochastic Partial Differential Equations and Applications II: Proceedings of a Conference Held in Trento, Italy, February 1-6, 1988

ISBN-13: 9783540515104 / Angielski / Miękka / 1989 / 268 str.

Giuseppe Da Prato; Luciano Tubaro

Opis

Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.

Spis treści

A covariant Feynman-Kac formula for unitary bundles over euclidean space.- On the integrated formulation of Zakai and Kushner equations.- Lattice approximation in the stochastic quantization of (?4)2 fields1.- The support of the density of a filter in the uncorrelated case.- Variational inequalities for the control of stochastic partial differential equations.- Generalized solutions of stochastic evolution equations.- On the relation of anticipative Stratonovich and symetric integrals: A decomposition formula.- Some applications of quantum probability to stochastic differential equations in Hilbert space.- The stability of stochastic partial differential equations and applications. Theorems on supports.- Weak convergence of solutions of stochastic evolution equations on nuclear spaces.- A stochastic reaction-diffusion model.- Stochastic partial differential equations of generalized Brownian functionals.- Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation.- A generalized equation for a continuous measure branching process.- Mesures cylindriques et distributions sur l'espace de Wiener.- A summary of some identities of the Malliavin calculus.- A Lie algebraic criterion for non-existence of finite dimensionally computable filters.- A generalization of Wahba's theorem on the equivalence between spline smoothing and Bayesian estimation.- A connection between the expansion of filtrations and Girsanov's theorem.- White noise in space and time as the time-derivative of a cylindrical Wiener process.- Large deviations for non-linear radonifications of white noise.- Symmetric solutions of semilinear stochastic equations.