摘要:

In this article, the Malliavin calculus is used to derive regularity properties of the conditional distribution of one ltd process given a second Ito process. The relation between the processes involved is the usual one assumed in the study of filtering theory. The non-degeneracy which we require is stated in terms of Malliavins covariance matrix in Theorem (3.15). More practical conditions are given in Lemma (3.19) for general Tto processes and in Lemma (3.29) for diffusions. Finally, in Theorem (4.6) a “localized” version of these results is given for diffusions.

ISSN:0090-9491    

DOI:10.1080/17442508408833296

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

摘要:

Given p≧1, letXbe a real-valued, continuousN-parameter process, submitted to a “domination condition” which ensures the existence of itskth variations μX(k) 1≦k≦k0p-stochastic measures which are the multi-parameter analogues of the “variation”dXand the “quadratic variation” d[X] of one-parameter semimartingales. This condition is fulfilled for example for processes of integrable variation, for the (N,1)-Wiener process W,or, more generally in case N=2, for those “representable semimartingales” (Wong Zakai or Guyon, Prum) which have sufficiently well-behaved representing functionals. Furthermore, it allows us to establish a stochastic calculus in Lpsense forXwith a simple version of Itô's formula in terms of the integrals ofμX(k),1≦k≦k0.

ISSN:0090-9491    

DOI:10.1080/17442508408833297

出版商:Gordon and Breach Science Publishers Inc    

年代:1984

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442508408833295

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

年代:1984

数据来源: Taylor