INCOMPATIBLE STOCHASTIC-PROCESSES AND COMPLEX PROBABILITIES

The definition of conditional probabilities is based upon the existenc e of a joint probability, However, a reconstruction of the joint proba bility from given conditional probabilities imposes certain constraint s upon the latter, so that if several conditional probabilities are ch osen arbitrarily, the corresponding joint probability may not exist. S uch an incompleteness in conditional probabilities can be eliminated b y introducing complex probabilities. The physical meaning of the new m athematical formalism, as well as its relation to quantum probabilitie s, is discussed. (C) 1998 Elsevier Science B.V.