Where one reads

“Note that between any two upcrossings there is a downcrossing and, similarly, there is a downcrossing between any two upcrossings.”

Shouldn’t it be

Note that between any two upcrossings there is a downcrossing and, similarly, there is a upcrossing between any two downcrossing.

?

]]>This is my expert

]]>This is my expert

]]>Thanks a lot for the interesting blog. Concerning Theorems 1 and 2, I was looking for references in the literature, but so far I haven’t found any. Can you help here?

Marcus

]]>You define a predictable sigma-algebra on {{\mathbb R}_+\times\Omega}, denoted by {\mathcal{P}} to be the sigma algebra generated by the left-continuous and adapted processes. You also write that a adapted process is one which in turn depends on the sigma algebra i.e that each r.v is measuable. This seems circular to me, do you mean that we take a left contious processes and then generate it’s natural filtration? Or have I gotten something wrong?

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