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Stochastic Calculus Question
Suppose is a Ito process and a stochastic process. And suppose , question:Does the following hold?the convergence is in the sense of "converge in probability", where n is send to infinity.If it holds, how do we demonstrate that, I probably need this proof, any indication or reference to any books is appreciated.Thank you in advance.
Stochastic Calculus Question
Such problems is usually proved by assuming 1st that H is uniformly bounded by non random a constant stepwise function. Then we need iniform integrable statement of the sum of the differences ( X ( i+1) - X ( i ) )^2 - <X , X > . For say Wiener process it follows from existing higher moments. Next limit transitions for N can be done by remark that prob that H larger than N can be make as small as we wish when N sufificiently large.
Last edited by list on July 2nd, 2012, 10:00 pm, edited 1 time in total.