Absolutely continuous change of measure in stochastic differential equations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Григелионис. Об абсолютно непрерывной замене меры и марковском свойстве случайных процессов B. Grigelionis. Apie absoliučiai tolydinį mato pakeitimą ir atsitiktinių procesų Markovo savybę

Download Full-text

On optimal controls in the problem of locally absolutely continuous change of measure (compact sets of decisions)

Vol. 1 ◽

10.1515/9783112319000-024 ◽

1987 ◽

pp. 331-356

Keyword(s):

Optimal Controls ◽

Compact Sets ◽

Continuous Change ◽

Change Of Measure ◽

Absolutely Continuous

Download Full-text

Stochastic differential equations with boundary conditions and the change of measure method

Stochastic Partial Differential Equations ◽

10.1017/cbo9780511526213.002 ◽

1995 ◽

pp. 1-21

Author(s):

Aureli Alabert

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Stochastic Differential Equations ◽

Change Of Measure

Download Full-text

STATISTICAL CAUSALITY AND MARTINGALE REPRESENTATION PROPERTY WITH APPLICATION TO STOCHASTIC DIFFERENTIAL EQUATIONS

Bulletin of the Australian Mathematical Society ◽

10.1017/s000497271400029x ◽

2014 ◽

Vol 90 (2) ◽

pp. 327-338 ◽

Cited By ~ 1

Author(s):

LJILJANA PETROVIĆ ◽

DRAGANA VALJAREVIĆ

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Continuous Time ◽

Change Of Measure ◽

Statistical Concept ◽

Martingale Representation ◽

Continuous Semimartingale ◽

Probability Spaces ◽

Definition Of ◽

Securities Trading

AbstractThe paper considers a statistical concept of causality in continuous time between filtered probability spaces, based on Granger’s definition of causality. This causality concept is connected with the preservation of the martingale representation property when the filtration is getting smaller. We also give conditions, in terms of causality, for every martingale to be a continuous semimartingale, and we consider the equivalence between the concept of causality and the preservation of the martingale representation property under change of measure. In addition, we apply these results to weak solutions of stochastic differential equations. The results can be applied to the economics of securities trading.

Download Full-text