论文标题
在ITô公式上进行跳跃过程
On Itô formulas for jump processes
论文作者
论文摘要
重新审视并修订了一个以随机积分相对于Wiener过程和泊松随机度量给出的有限维度过程的众所周知的ITô公式。然后，修订后的公式对应于具有跳跃的Semimartingales的经典itôula公式，然后用于获得对Krylov证明的重要无限尺寸iTôula的概括，用于连续的Semimartingales，以对一类$ l_p $ l_p $的跳跃过程证明。这种概括是由随机PDE理论中的应用激发的。
A well-known Itô formula for finite dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical Itô formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite dimensional Itô formula for continuous semimartingales proved by Krylov to a class of $L_p$-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.
