A weak convergence criterion for constructing changes of measure

作者：Blanchet Jose; Ruf Johannes^*

来源：Stochastic Models, 2016, 32(2): 233-252.

DOI：10.1080/15326349.2015.1114891

• Conditional queuing process
• existence of weak solution
• Girsanov theorem
• local martingale
• tightness

Based on a weak convergence argument, we provide a necessary and sufficient condition that guarantees that a nonnegative local martingale is indeed a martingale. Typically, conditions of this sort are expressed in terms of integrability conditions (such as the well-known Novikov condition). The weak convergence approach that we propose allows to replace integrability conditions by a suitable tightness condition. We then provide several applications of this approach ranging from simplified proofs of classical results to characterizations of processes conditioned on first passage time events and changes of measures for jump processes.

• 出版日期2016