Brownian Motion and Stochastic Calculus
نویسنده
چکیده
This note is about Doob decomposition and the basics of Square integrable martingales Contents 1 Doob-Meyer Decomposition 1 2 Square Integrable Martingales 4 Brownian Motion and Stochastic Calculus Continuout Time Submartingales Usually its su¢ ce to only discuss submartingales by symmetry in de nition and techniques are the same. 1 Doob-Meyer Decomposition Doob-meyer decomposition clears the obstable for de ning stochastic integral (in the isometry strategy) wrt square integrable martingales and hence is of foundamental importance De nition 1 An increasing process A is called natural if for every bounded, right continuous martingale fMt;Ft : 0 t <1g we have E Z
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