摘要:

In 1969 N. V. Krylov obtained the following estimatewhereXis an Ito process inis the exit time ofXfrom a bounded regionis Ld-norm of a measurable nonnegative function , and N is a constant. We generalize estimates of this type to semimartingales and give applications to the theory of stochastic equations with respect to semimartingales. The questions of the existence, uniqueness, convergence and comparison of solutions of these equations are also studied.

ISSN:0090-9491    

DOI:10.1080/17442508308833265

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

We find the solution to the finite fuel problem of optimally controlling a diffusionso as to maximise EC(ρ) where ρ is the first time Xtgoes below zero.

ISSN:0090-9491    

DOI:10.1080/17442508308833266

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

The aim of this paper isto give a characterization theorem for Gaussian processes.It is wellknown that for Gaussian processes the conditional expectation is alinear function of the states of the process and the conditionalvariance is a deterministic function. In the presentpaper we show aconverse implication. We prove that these two conditions and Lipschitz condition for the covariance function characteristicGaussian processes. The proof is based on a limit theorem for sums ofdependent random variables.

ISSN:0090-9491    

DOI:10.1080/17442508308833267

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508308833268

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

摘要:

Let Pεbe the iaw of the 1-dim diffusion with generatorwhere a > 0 and a, b are bounded continuous functions. We use a Tauberian theorem to construct an example that {Pε}ε>0 fails to have an unique limit point if b does not satisfy the Lipschitz condition.

ISSN:0090-9491    

DOI:10.1080/17442508308833269

出版商:Gordon and Breach Science Publishers Inc,    

年代:1983

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508308833264

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

年代:1983

数据来源: Taylor