ON THE STOCHASTIC DIFFERENTIAL EQUALITIES

We give a new sense of stochastic differential equalities. We show that if there exists a stochastic process B which satisfies a set of conditions forming what we called ‘the H hypothesis’, then B could play the same part as the Brownian motion in stochastic calculus and a series of results known in this calculus can be rigorously proved. This new theory is not a formal generalization of the stochastic calculus, it has distinct basis and it develops itself by means of its own tools.