Geodesic
Statistical causality and adapted distribution
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 827-843

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept of causality between stochastic processes, which is based on Granger's definition of causality. Also, we provide applications of our results to solutions of some stochastic differential equations.
DOI : 10.1007/s10587-011-0030-1
Classification : 03C98, 60G07, 60H10
Keywords: filtration; causality; adapted distribution; weak solution of stochastic differential equation 
@article{10_1007_s10587_011_0030_1,
     author = {Petrovi\'c, Ljiljana and Dimitrijevi\'c, Sladjana},
     title = {Statistical causality and adapted distribution},
     journal = {Czechoslovak Mathematical Journal},
     pages = {827--843},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {2011},
     doi = {10.1007/s10587-011-0030-1},
     mrnumber = {2853095},
     zbl = {1249.60063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0030-1/}
}
TY  - JOUR
AU  - Petrović, Ljiljana
AU  - Dimitrijević, Sladjana
TI  - Statistical causality and adapted distribution
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 827
EP  - 843
VL  - 61
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0030-1/
DO  - 10.1007/s10587-011-0030-1
LA  - en
ID  - 10_1007_s10587_011_0030_1
ER  - 
%0 Journal Article
%A Petrović, Ljiljana
%A Dimitrijević, Sladjana
%T Statistical causality and adapted distribution
%J Czechoslovak Mathematical Journal
%D 2011
%P 827-843
%V 61
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0030-1/
%R 10.1007/s10587-011-0030-1
%G en
%F 10_1007_s10587_011_0030_1
Petrović, Ljiljana; Dimitrijević, Sladjana. Statistical causality and adapted distribution. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 827-843. doi: 10.1007/s10587-011-0030-1

Cité par Sources :