Thanks again,

Alessandro

Thanks for the great blog! During my study of general semimartingale theory, I often encounter the notion of Dirichlet process, a strict superset of the set of semimartingales. Is it possible that you write something on this subject? Namely, I was curious if one can develop theory of stochastic integration w.r.t. Dirichlet process. In addition, I was also curious if there is any simple characterization of Dirichlet processes( except that they are sum of local martingale and zero-energy process). I would like to know if every continuous adapted processes which are martingales under its natural filtration will be Dirichlet.

Thanks in advance and looking forward to your reply!

you say that all continuous adapted processes are locally bounded, with the localizing sequence you mentioned. I do not see how this sequence makes something bdd. I see that saying that absolute value is $\geq n$ makes only situation worse. I.e. all r.v.-s because of this of a process $X^\{tau_n} = { X^{t_1}_1,\ldots,X^{t_\infty}_{\infty}}$ are saying that each r.v. of this sequence are bdd from below!

Could you please shed some light on my basic, probably not smart, question? ]]>