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4. (Total: 20 marks) Let {Bt, t > 0} be a standard Brownian motion and 0(t1, t2) denote the event that the Brownian moti
Posted: Fri Dec 24, 2021 9:51 am
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- 4 Total 20 Marks Let Bt T 0 Be A Standard Brownian Motion And 0 T1 T2 Denote The Event That The Brownian Moti 1 (121.68 KiB) Viewed 100 times
4. (Total: 20 marks) Let {Bt, t > 0} be a standard Brownian motion and 0(t1, t2) denote the event that the Brownian motion process takes on the value 0 at least once in the interval (t1, t2), where t2 >tı > 0. Please compute the probability of 0(t1, t2). (Hint: Condition on the value of Bt, and then relate the event to the maximum variable of a Brownian motion.)