MARTINGALES ON JUMP PROCESSES .1. REPRESENTATION RESULTS

被引：75

作者：

BOEL, R

VARAIYA, P

WONG, E

机构：

[1] UNIV CALIF,DEPT ELECT ENGN & COMP SCI,BERKELEY,CA 94720

[2] UNIV CALIF,ELECTR RES LAB,BERKELEY,CA 94720

来源：

SIAM JOURNAL ON CONTROL | 1975年 / 13卷 / 05期

关键词：

INFORMATION THEORY - Filtering and Prediction Theory;

D O I：

10.1137/0313063

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A contribution is made to the theory of martingales of processes whose sample paths are piecewise constant and have finitely many discontinuities in a finite time interval. The assumption is made that the jump times of the underlying process are totally inaccessible and necessary and sufficient conditions are given for this to be true. It turns out that all martingales are then discontinuous, and can be represented as stochastic integrals of certain basic martingales. This representation theorem is used in a companion paper to study various practical problems in communication and control.

引用

页码：999 / 1021

页数：23

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