Stochastic Differential Systems -

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Résumé :
The 4th Bad Honnef Conference on Stochastic Differential Systems highlighted recent advances in the areas of stochastic control and filtering theory as well as stochastic analysis. Special emphasis was put on the use of adaptive methods in stochastic systems analysis and on the theory of random fields, both very active fields of current research. There were six survey lectures, two of them on adaptive control of linear stochastic systems (Kumar, Lai), two on problems in stochastic analysis and random fields, (Surgailis, Wong) and one on singular perturbations in nonlinear filtering (Bensoussan). In addition, 37 research papers pertaining to the main topics of the conference were presented.

Sommaire:
Some results on Newton equation with an additional stochastic force.- On dirichlet forms on topological vector spaces: Existence and maximality.- Nowhere Radon smooth measures, perturbations of Dirichlet forms and singular quadratic forms.- A generalization of Ito's formula.- General functional limit theorems for semimartingales.- Nonlinear filtering for dynamic systems with singular perturbations.- On recursive adaptive filtering: Linear case.- On the smooth fit boundary conditions in the optimal stopping problem for semimertingales.- Order determination and adaptive control of ARX models using the PLS criterion.- Adaptive control of some partially observed linear stochastic systems.- The adjoint process in stochastic optimal control.- Integration by parts and the Malliavin calculus.- Pathwise stability of random differential equations and the solution of an adaptive control related problem.- Stochastic analysis of intertemporal economic issues.- OLS-Estimation and rationality in linear models with forecast feedback.- Invariance of cones and comparison results for some classes of diffusion processes.- Performance and robustness in adaptive control of linear stochastic systems.- Singular perturbations for stochastic control.- Extended stochastic lyapunov functions and recursive algorithms in linear stochastic systems.- Consistency sets of least squares estimates in stochastic regression models.- Consistency of estimators in controlled systems.- Stochastic controllability and stochastic Lyapunov functions with applications to adaptive and nonlinear systems.- A simple stochastic growth model for filamentary current structures in semiconductor systems.- The rate of convergence and the asymptotic normality of an estimator in a controlled investment model with time-varying parameters.- On invariant measures of filtering processes.- Polygonal fields: A new class of markov fields on the plane.- Strictly stationary processes with the linear prediction property.- Multiparameter martingale and Markov process.- Limit theorems for storage process with the domain of attraction of a stable law.