On a dyadic approximation of predictable processes of finite variation

Pietro Siorpaes

On a dyadic approximation of predictable processes of finite variation

Probability 2014-03-28 v5

Authors: Pietro Siorpaes

Abstract

We show that any cadlag predictable process of finite variation is an a.s. limit of elementary predictable processes; it follows that predictable stopping times can be approximated `from below' by predictable stopping times which take finitely many values. We then obtain as corollaries two classical theorems: predictable stopping times are announceable, and an increasing process is predictable iff it is natural.

Keywords

predictable processes finite variation cadlag stopping times dyadic approximation natural processes announceable

Cite

@article{arxiv.1306.6238,
  title  = {On a dyadic approximation of predictable processes of finite variation},
  author = {Pietro Siorpaes},
  journal= {arXiv preprint arXiv:1306.6238},
  year   = {2014}
}

Comments

version 5: To make the paper more readable I made the paper more self contained, and I have changed the order with which theorems are stated and proved

On a dyadic approximation of predictable processes of finite variation

Abstract

Keywords

Cite

Comments

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