Grigelionis, Bronius; Mackevicius, Vigirdas - In: Statistics & Probability Letters 64 (2003) 3, pp. 243-248
It is well known that the stochastic exponential , of a continuous local martingale M has expectation EZt=1 and, thus, is a martingale if (Novikov's condition). We show that, for p1, EZtp<[infinity] if Eexp{cp<M>t}<[infinity] with , and the result is optimal in the sense that cp cannot be replaced by any cp-[var epsilon] with [var epsilon]>0. As a consequence, we get that the moments of the stochastic exponential of a stochastic integral with...</[infinity]></[infinity]>