The Structure of Local Martingles

1. On page 186. in the proof of Proposition 3.15. the usual way means that first one applies the Monotone Class Theorem to get the proposition for bounded X. Then one applies the bounded case for the cutted processes, where a cutted process is X whenever X is smaller than n otherwise it is n. Then one applies that the limit of measurable functions is measurable.

2. On page 200 in the second line of the proof of Proposition 3.35 in the definition of the stopping time one should change the strict ineguality > to >= otherwise the proof is not working in the case when some trajectories absolute value have a local maximum with value n. In this case the graph of the stopping times will be not given in a way assummed in the 7th line of the proof.

3. On page 208 in the Generalized Radon-Nikodym Theorem one can only have that A has finite variation and the theorem is not true for locally integrable processes. The best example is if the random measure is already in the given form, but the integrator process is not locally integrable. On page 216 one should recall that every predictable, right-regular process is locally bounded by Proposition 3.35.

ch3.txt · Utolsó módosítás: 2011/01/02 08:07 szerkesztette: medvegyev
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