摘要:

In the second part of this study a general Itô formula is proved in Banach spaces. A special case reads as follows.

ISSN:0090-9491    

DOI:10.1080/17442508208833202

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508208833203

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

We establish equations of non linear filtering, prediction (extrapolation) and smoothing (interpolation) in the case where the signal is a non degenerate diffusion process, and the observation is a noisy functional of the signal. We consider both the case of observation noise correlated with the signal, and the opposite case where we establish “robust” form of the equations. We study finally the case of unbounded coefficients, and the case where there is a feedback from the observation to the signal.

ISSN:0090-9491    

DOI:10.1080/17442508208833204

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

An elementary argument is used to show that the Markov semigroup of a stochastic dynamical system which has a flow consisting of diffeomorphisms necessarily preserves the space of continuous functions vanishing at infinity. In the one dimensional case this is seen to be also a sufficient condition. As a corollary there is a result proved by Kunita under slightly stronger conditions on the coefficients: a non-degenerate system on R has a flow consisting of homeomorphisms if and only if both ± ∞ are natural boundaries.

ISSN:0090-9491    

DOI:10.1080/17442508208833205

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

Levy's modulus of continuity is proved for infinite dimensional Wiener processes. Using the loglog law for a Banach space valued Wiener process in [7], we prove the loglog law for Hilbert space valued stochastic integrals, if the integrand is Holder continuous. From a corollary of Kolmogorov's law we derive the Hölder continuity of Hilbert space valued stochastic integrals if the fourth moment of the integrand is uniformly bounded. As an application we show that the mild solution of a stochastic evolution equation has a continuous version if the semigroup governing this equation is analytic.

ISSN:0090-9491    

DOI:10.1080/17442508208833206

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

Let {x∈(·)} be a sequence of solutions to an ordinary differential equation with random right sides (due to input noise {ξ∈(·)}) and which converges weakly to a diffusionx(·) with unique invariant measure µ(.). Let µ(t,·) denote the measure ofx(t), and suppose that µ(t,·)-?µ(·) weakly. The paper shows, under reasonable conditions, that the measures ofx(t) are close to µ(·) for largetand small ∈. In applications, such information is often more useful than the simple fact of the weak convergence. The noise ξ∈(·) need not be bounded, the pair (x∈(·), ξ(·)) need not be Markovian (except for the unbounded noise case), and the dynamical terms need not be smooth. The discrete parameter case is also treated, and several examples arising in control and communication theory are given.

ISSN:0090-9491    

DOI:10.1080/17442508208833207

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

LetPεbe the law of the diffusion inwhose differential generator is given by, where b is a continuous function. We study the limiting values ofin case the ordinary differential equationx′(t) =b(x(t)) has Peano phenomenon and, in particular,bdoes not satisfy a Lipschitz condition.

ISSN:0090-9491    

DOI:10.1080/17442508208833208

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

摘要:

Given a forward ( = usual) stochastic differential equation (SDE), we consider, in this paper, an associated backward SDE. Let E;s,t(x),t∈[s, ∞) be the solution of an SDE on a manifold M:with the initial condition ξs,s(x) =x. HereX0,…,Xrare smooth vector fields, (Bt1,…,Bt1) is a standard r-dimensional Brownian motion and o denotes the Stratonovich integral. We show that the solution E;s,tsatisfies the backward SDE:where ξstthe differential of the map Es,t(·)M→Mand [dcirc]Bsjdenotes the backward stochastic integral. The result is applied to getting a necessary and sufficient condition that the map ξs,t: defines a diffeomorphism ofMa.s.

ISSN:0090-9491    

DOI:10.1080/17442508208833209

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508208833210

出版商:Gordon and Breach Science Publishers Inc    

年代:1982

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508208833201

出版商:Gordon and Breach Science Publishers S. A.    

年代:1982

数据来源: Taylor