thank you for your answer, but we start with local martingal and dont have all martingal properties.
E[X_t-X_s]=0 for some stopping time, which u did not consider.
"V[s,t]=int|X_u| du< Infinity implies int (X_u)du < Infinity" for every finite interval P.a.s is given, but what do you mean by X'_u, how is it definded?
E[X_t-X_s]=E int (X'_u) du, why ist that true?
stoch process does not have nessecarilly a derivative, you mean increment?
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