Brownian bridge
Question 1. Brownian bridge [11 marks] Consider the process X_t=B_t-tB_1,0≤t≤1, where B_t is a standard Brownian Motion. Show that X_t is a standard Brownian bridge [2 marks]. Determine E[exp(〖1/2 X〗_(3⁄10)+〖2/3 X〗_(7⁄10) )] [3 marks]. Show that E[X_(7⁄10)∨X_(3⁄10) ]=3/7 X_(3⁄10) [3 marks]. Using the result from (c), determine E[X_(3⁄70)^2 X_(7⁄10) ] [3 marks]. … Read more