On Jump Measures of Optional Processes with Regulated Trajectories

2015/08/09 by Frank Oertel, Oertel, Frank
Mathematics · #60G05 #60G57 #91G40 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G05 #msc:60G57 #msc:91G40

paper · pdf · doi:10.48550/arxiv.1508.01973

arXiv admin note: text overlap with arXiv:math/0609395

arxiv created 2015/08/09 · arxiv updated 2015/08/11

Abstract

Starting from an iterative and hence numerically easily implementable representation of the thin set of jumps of a càdlàg adapted stochastic process X (including a few applications to the integration with respect to the jump measure of X), we develop similar representation techniques to describe the set of jumps of optional processes with regulated trajectories and introduce their induced jump measures with a view towards the framework of enlarged filtration in financial mathematics.

Citations

• On random measures, unordered sums and discontinuities of the first kind

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