论文标题
随机积分和两个过滤
Stochastic Integrals and Two Filtrations
论文作者
论文摘要
在随机积分的定义中，除了集成和整合器外，还有一种起作用的基本过滤。 Thus, it is natural to ask: {\it Does the stochastic integral depend upon the filtration?} In other words, if we have two filtrations, $({\mathcal F}_\centerdot)$ and $({\mathcal G}_\centerdot)$, a process $X$ that is semimartingale under both the filtrations and a process $f$ that is predictable for both the过滤，然后是两个随机积分 - $ y = \ int f \，dx $，带过滤$（{\ Mathcal f} _ \ centerDot）$和$ z = \ int f \，dx $，带有过滤$（{\ nathcal g} _ \ centerdot）$相同？ 当$ f $连续以右限制连续时，答案是肯定的。当一种过滤是另一个过滤的扩大时，如果$ f $有限，则两个积分相等，但是当$ f $不受限制时可能不是这种情况。 我们讨论了这一点，并提供了两个积分相等的条件。
In the definition of the stochastic integral, apart from the integrand and the integrator, there is an underlying filtration that plays a role. Thus, it is natural to ask: {\it Does the stochastic integral depend upon the filtration?} In other words, if we have two filtrations, $({\mathcal F}_\centerdot)$ and $({\mathcal G}_\centerdot)$, a process $X$ that is semimartingale under both the filtrations and a process $f$ that is predictable for both the filtrations, then are the two stochastic integrals - $Y=\int f\,dX$, with filtration $({\mathcal F}_\centerdot)$ and $Z=\int f\,dX$, with filtration $({\mathcal G}_\centerdot)$ the same? When $f$ is left continuous with right limits, then the answer is yes. When one filtration is an enlargement of the other, the two integrals are equal if $f$ is bounded but this may not be the case when $f$ is unbounded. We discuss this and give sufficient conditions under which the two integrals are equal.
