The aim of this paper is to demonstrate by examples the possible "extreme" behaviour of exponential moments of two Brownian functionals. As a consequence, it will follow that the "uniform" Novikov condition does not imply the condition and vice versa. Both conditions (1) and (2) are known to be...

Let X be a seminmartingale and Teta the space of all predictable X-integrable processes teta such that integral tetat dX is inthe space S square of semimartingales. We consider the problem of approximating a given random variable H element of L square (P) by the sum of a constant c and a...

We describe a method of approximation of strong solutions to Stratonovich differential equations, that depends only on the Brownian motion defining the equation. h being the step size, it is known that the order of convergence of such approximations is h in the general case, and of h in some...