Valjarevic D.   Ljajko E.   Jovanovic T.  

Theory of Statistical Causality and Quasimartingales

Reporter: Valjarevic D.

Concept of causality is very popular and applicable nowadays. Especially when we consider the cases “what would happen if” and “what would have happened if”. Here we consider the concept of causality based on the Granger’s definition of causality, introduced by P.A. Mykland in [1]. Many of the systems to which it is natural to apply tests of causality take place in continuous time, so we will consider the continuous time processes. The given concept of causality is closely connected to the preservation of the martingale property. Here we consider its connection to the property of being a quasimartingale. Quasimartingales were investigated by D.L. Fisk [2], S.Orey and specially K.M.Rao [3]. Namely we proved an equivalence between the given concept of causality and preservation of the quasimartingale property if the filtration is getting larger.

References
[1] P. A. Mykland, “Statistical Causality,” Statistical Report, No.14, University of Bergen, 1-14, (1986).
[2] D. L. Fisk, “Quasi-martingales,” Trans. Amer. Math. Soc. 120, 369-389, (1965).
[3] K. M. Rao; “Quasi-martingales,” Math. Scand. 24, 79-92, (1969).