摘要:

The original proof of the Central limit theorem for Lorentz gas was given by L. A.Bunimovich and Ya. G. Sinai in 1981. In this paper a much more concise proof using Donsker's invariance principle for martingales is given.

ISSN:0090-9491    

DOI:10.1080/17442508408833328

出版商:Gordon and Breach Science Publishers, Inc    

年代:1984

数据来源: Taylor

摘要:

All nontrivial solutions of x = A(t)x grow exponentially with rate X(x,w)e{A1,...,Xr}, A a (strictly) stationary matrix process. Projecting x to the unit sphere one obtains for each of the Lyapunov exponents Xt a solution xt with stationary angle st. Now if A is a Markov process one can restrict oneself to Markov solutions, i.e., (x, A) shall be a (joint) Markov process (wich is a restriction on the inital conditions). We prove that whenever there is a Markov solution x with Lyapunov number X then there is another Markov solution with a stationary angle (or equivalently: an invariant measure for the transition probabilities of (s, A)) with the same Lyapunov number. This has some consequences, e.g., for the uniqueness of the Lyapunov numbers

ISSN:0090-9491    

DOI:10.1080/17442508408833329

出版商:Gordon and Breach Science Publishers, Inc    

年代:1984

数据来源: Taylor

摘要:

One of the main results of [2] shows that neither the Weyl algebra An, nor any (Lie Algebra) quotient of A can be realised as analytic vector fields on a finite dimensional manifold. In this note we give an elementary proof of this fact. This is related to the non-existence of finite dimensional recursive filters for certain problems in non-linear filtering theory, notably the cubic sensor problem (see [2,3 and 4]). The methods used here also show that the Weyl algebra has no sub-Lie algebra of finite codimension.

ISSN:0090-9491    

DOI:10.1080/17442508408833330

出版商:Gordon and Breach Science Publishers, Inc    

年代:1984

数据来源: Taylor

摘要:

Evolution of interacting particles in a random medium is studied by treating their spatial distribution as a measure-valued process. Each individual particle is assumed to move according to a stochastic differential equation, the interaction being manifest both through the correlation of the driving Wiener processes and through the explicit dependence of the “drift” and “diffusion” coefficients on the overall distribution of the particles. The evolution equation for the above-mentioned measure-valued process is derived and the uniqueness of its solutions established using the techniques developed by Bismut and Kunita.

ISSN:0090-9491    

DOI:10.1080/17442508408833331

出版商:Gordon and Breach Science Publishers, Inc    

年代:1984

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508408833332

出版商:Gordon and Breach Science Publishers, Inc    

年代:1984

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508833327

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor