Statistics of random processes tome I - General theory

Robert S. Liptser, Albert N. Shiryaev - Collection Applications of mathematics

428 pages, parution le 19/04/2004

Ajouter à une liste

Indisponible

Résumé

The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.

Sommaire

Essentials of probability theory and mathematical statistics.
Martingales and related processes.
Martingales and supermartingales: continuous time.
The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations.
Square integrable martingales, and structure of the functionals on a Wiener process.
Nonnegative supermartingales and martingales, and the Girsanovs theorem.
Absolute continuity of measures corresponding to the Ito processes and processes of diffusion type.
General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes.
Optimal filtering, interpolation and extrapolation of Markov processes with countable number of states.
Optimal linear nonstationary filtering.

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Robert S. Liptser, Albert N. Shiryaev
Collection	Applications of mathematics
Parution	19/04/2004
Nb. de pages	428
Format	16 x 24
Couverture	Relié
Poids	767g
Intérieur	Noir et Blanc
EAN13	9783540639299