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Towards a general Doob-Meyer decomposition theorem

100%

Jakubowski A.

Probability and Mathematical Statistics

2006

tom Vol. 26, Fasc. 1

143--153

Both the Doob-Меуег and Graversen-Rao decomposition theorems can be proved following an approach based on predictable compensators of discretizations and weak-L1 technique, which was developed by K. M. Rao. It is shown that any decomposition obtained by Rao’s method gives predictability of compensators without additional assumptions (like submartingality in the original Doob-Meyer theorem or finite energy in the Graversen-Rao theorem).

Proposition of Stochastic Postulates for Chain Indices

100%

Białek J.

Statistics in Transition new series

2014

tom 15

nr 4

545_558

This article presents and discusses a proposition of stochastic postulates for chain indices. The presented postulates are based on the assumption that prices and quantities are stochastic processes and we consider also the case when price processes are martingales. We define general conditions which allow the chain indices to satisfy these postulates.

Note on the selection properties of set-valued semimartingales

100%

Michta M.

nr 2

161-169

Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.

Principle of Conditioning revisited

75%

Jakubowski A.

2012

tom Vol. 45, nr 2

325-336

Principle of Conditioning is a well known heuristic rule which allows constructing limit theorems for sums of dependent random variables from existing limit theorems for independent summands. In the paper we state a general limit theorem on converegnce to stable laws, which is valid for stationary sequences and provides a link between the Principle of Conditioning and ergodic theorems.