标题： 诺维科夫型条件用于带跳的局部鞅：最优性与初等证明 显示英文标题

标题： Novikov-type criteria for local martingales with jumps: Optimality and elementary proofs

摘要： 我们考虑具有大于$a$的跳跃的局部鞅 M，其中$a$大于或等于 -1，并证明了指数局部鞅成为一致可积鞅的诺维科夫型条件。 我们使用二次变差和可预测二次变差来获得条件。 我们证明了条件中系数的最优性。 作为推论，我们得到了经典诺维科夫条件对于连续局部鞅的原样扩展到具有非负跳跃的局部鞅的情况。 此外，我们给出了新的扩展诺维科夫型条件的初等证明，这些条件要求二次变差和可预测二次变差的凸组合的指数矩。 显示英文摘要

摘要： We consider local martingales M with jumps larger than $a$ for some $a$ larger than or equal to -1, and prove Novikov-type criteria for an exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a corollary, we obtain a verbatim extension of the classical Novikov criterion for continuous local martingales to the case of local martingales with nonnegative jumps. Also, we give elementary proofs of new extended Novikov-type criteria, requiring an exponential moment of a convex combination of the quadratic variation and the predictable quadratic variation.