Question: Let Bt, t 2 0, be Brownian motion started at 0. (1) Write Ito formula for Be, specifying f (x) and its two derivatives. (2)

Let Bt, t 2 0, be Brownian motion started at 0.

Let Bt, t 2 0, be Brownian motion started at 0. (1) Write Ito formula for Be, specifying f (x) and its two derivatives. (2) Show that the process Yt in the following identity is a martingale: = 6 B'sds + Yt. (3) Prove or dis-prove by a way of a counter example the following statements: (a If Xt > Y't then So Xtdt > So Ydt. (b) If Xt > Yt then So XtdBt > So VidBt

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