摘要:

We present a nonrandom version of the Multiplicative Ergodic (Oseledec) Theorem for a nonlinear stochastic dynamical system on a smooth compact Riemannian Manifold M. This theorem characterises the a.s. asymptotic behaviour of the derivative system. Our approach (based on work of Furstenberg and Kifer, who deal with a linear system) is to consider an associated system on the projective bundle over M and to relate the behaviour of the theorem to the ergodic behaviour of this system. When the system has no random element, our work reduces to an alternative approach to the Multiplicative Ergodic Theorem for a diffeomorphism of M.

ISSN:0090-9491    

DOI:10.1080/17442508608833393

出版商:Gordon and Breach, Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

Nonlinear smoothing algorithms are studied where the white noise disturbance in the observation is treated directly, instead of the usual modelling through its integrated version of Brownian motion. This framework yields results already in the robust form. Furthermore, the Itô integrals involving the observations do not appear in this approach, thereby eliminating complications arising out of considering backward Itô integrals in the smoothing problems.

ISSN:0090-9491    

DOI:10.1080/17442508608833394

出版商:Gordon and Breach, Science Publishers, Inc    

年代:1986

数据来源: Taylor

摘要:

The nonlinear filtering problem for a diffusion process whose drift and diffusion coefficients depend parametrically on a finite-state jump process involves the solution of a vector system of linear, stochastic partial differential equations. A Lie-Trotter product formula is proven to hold for this system and a recursive implementation is discussed.

ISSN:0090-9491    

DOI:10.1080/17442508608833395

出版商:Gordon and Breach, Science Publishers, Inc    

年代:1986

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508608833392

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor