Vol.4, No 17, 2005 pp. 293-300
UDC 517.9:519.856(045)=20
SOME MODELS OF CAUSALITY AND
STOCHASTIC DIFFERENTIAL EQUATIONS
Ljiljana Petrović
Faculty of Economics, Belgrade, Kamenička 6
Abstract. We consider some concepts of causality between
sigma-algebras
and between stochastic processes. Then, we give a generalization of a
causality
relationship "G is a cause of E within H" which was first given by
Mykland
[4] and which is based on Granger's definition of causality [1].
In the second part we apply the results to systems of stochastic
differential
equations. More precisely, we give conditions for weakly uniqueness of
the solution of some stochastic differential equations.
Key words: sigma-algebra, causality, weak solution of stochastic
differential equation
NEKI MODELI UZROČNOSTI I STOHASTIČKE
DIFERENCIJALNE
JEDNAČINE
U radu se razmatraju neki koncepti uzročnosti izmedju sigma-algebra i
između
stohastičkih procesa. Zatim se navodi generalizacija relacije
uzročnosti
�G je uzrok E u okviru H�, koju je prvi dao Mykland [4] i koja se
zasniva
na Granger-ovoj definiciji uzročnosti [1]. U drugom delu rada rezultati
se primenjuju na sisteme stohastičkih diferencijalnih jednačina.
Preciznije,
daju se uslovi za slabu jedinstvenost rešenja nekih stohastičkih
diferencijalnih
jednačina.
Ključne reči: sigma-algebra, uzročnost, slabo rešenje
stohastičke
diferencijalne jednačine.
