Question: 3.5. Determine the expected value for absorbed Brownian motion A(t) at time t = 1 by integrating the transition density (3.6) according to The answer

3.5. Determine the expected value for absorbed Brownian motion A(t)

at time t = 1 by integrating the transition density (3.6) according to

E[A(1) A(0) = x] = y p(y, 1x) dy = { =

The answer is E[A(1)IA(0) = x] = x. Show that E[A(t)IA(0) = x] = x for all t > 0.

E[A(1) A(0) = x] = y p(y, 1x) dy = { = 0 - - y[oy x) (y + x)] dy.

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