Statistical causality and adapted distribution

Ljiljana Petrović; Sladjana Dimitrijević

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 3, page 827-843
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Petrović, Ljiljana, and Dimitrijević, Sladjana. "Statistical causality and adapted distribution." Czechoslovak Mathematical Journal 61.3 (2011): 827-843. <http://eudml.org/doc/197110>.

@article{Petrović2011,
abstract = {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.},
author = {Petrović, Ljiljana, Dimitrijević, Sladjana},
journal = {Czechoslovak Mathematical Journal},
keywords = {filtration; causality; adapted distribution; weak solution of stochastic differential equation; filtration; causality; adapted distribution; weak solution of stochastic differential equation},
language = {eng},
number = {3},
pages = {827-843},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Statistical causality and adapted distribution},
url = {http://eudml.org/doc/197110},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Petrović, Ljiljana
AU - Dimitrijević, Sladjana
TI - Statistical causality and adapted distribution
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 827
EP - 843
AB - 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.
LA - eng
KW - filtration; causality; adapted distribution; weak solution of stochastic differential equation; filtration; causality; adapted distribution; weak solution of stochastic differential equation
UR - http://eudml.org/doc/197110
ER -

References

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