摘要:

IfFis a Frechet differentiable functional onis a Brownian motion, andclark's formula states thatwhereis the measure defining the Frechet derivative ofFatb.In this paper we extend Clark's formula to the more general class of weaklyH-differentiablefunctionals, and we give a simple proff based on Malliavin's calculus. again using Malliavin calculus techniques, we also derive Haussmann's stochastic integral representation of a functionF(y) of the diffusion processIn doing this, we show that is weaklyH-differentiable if m and have bounded, continuous, first derivatives iny.

ISSN:0090-9491    

DOI:10.1080/17442508408833299

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

We consider the Cauchy problem for the stochastic differential equation with the heredity wherext(s) =x(s)forsε(- ∞,t).Existence and uniqueness theorems for the problem (1),(2)are proved inthe case,when instead of the Lipschitz condition for the functionsa(t,u)andb(t,u)on u someless restrictive conditions (Ousgood or Hölder type)are satisfied, and the operator(Fx)(t) =x(t)-f(t,xt) is invertible.Similar questions were considered in[1-4]

ISSN:0090-9491    

DOI:10.1080/17442508408833300

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

Parameter identification is studied for infinite dimensional linear systems. An almost sure characterization of sample path-wise limit sets of maximum likelihood estimates is given.

ISSN:0090-9491    

DOI:10.1080/17442508408833301

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

We consider a linear system with additive noise in Hilbert space and minimize a convex functional associated with this process. A necessary and sufficient condition for a control to be optimal is derived by evaluating the subdifferential of the cost function. Then the subdifferential of the value function is characterized. Finally using these results and a conditional value function, optimal controls are characterized as a feedback law in terms of the value function.

ISSN:0090-9491    

DOI:10.1080/17442508408833302

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

We study questions of existence and uniqueness for one-dimensional stochastic differential equations driven by a Brownian motion and an increasing process. It is shown that under fairly general conditions on the diffusion coefficient, if the drift coefficient is cadlag in x and has only positive jumps, then maximal and minimal strict solutions exist. If the drift coefficient has negative jumps, then the stochastic differential equation need not have a solution on any space. We give an example showing that the maximal and minimal solutions may be distinct as soon as the classical Lipschitz condition on the drift coefficient is weakened.

ISSN:0090-9491    

DOI:10.1080/17442508408833303

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

The stochastic differential equations with a small parameter ϵ, which for ϵ=0 degenerate into a dynamical system with a repulsive type stationary point, are considered. The asymptotic behavior of the exit point distributions of the solution of these equations is described. An example when these distributions diverge is exhibited. This also gives the asymptotic behavior of the solutions of the corresponding perturbed Dirichlet problem.

ISSN:0090-9491    

DOI:10.1080/17442508408833304

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

A stability theorem for stochastic differential equations is used to prove a result similar to one of Gangolli: letNbe Riemannian manifold with the Levi-Civita connection, and let (Cn(t), O≦t≦T) be a provess on N obtained by projecting a Brownian motion in the tangent space at Cn(jT/n) on to N during the time interval jT/n≦t<(j+l)T/n. Then there is a Brownian motion onNto which Cnconverges uniformly in probability

ISSN:0090-9491    

DOI:10.1080/17442508408833305

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

We consider the diffusion dx(t) = b{x(t))dt-\-y/sa(x(t))dw in a domain D which is contained in the domain of attraction of an asymptotically stable critical point of x = b(x). Using a formula of Hasminskii for the equilibrium measure of x(-) we show that the asymptotic behaviors of the exit measure P[x?{i:D)edy] and the equilibrium density pE(y) are connected. The formula connecting the two is essentially the same as one derived by Matkowsky and Schuss using formal methods. The treatment here provides probabilistic insight into the Matkowsky-Schuss formula.

ISSN:0090-9491    

DOI:10.1080/17442508408833306

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508408833298

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

年代:1984

数据来源: Taylor