Question

Use Matlab. I want a html.

3. (5) For a random walk on the set = {0,1, 2,... , a}, with probability that p 0.51 of taking a step to the right, let ha denote the probability that the walk will reach a before reaching 0. (a) Calculate ha by Markov chain methods. (b) Use simulation to estimate h

Answer 1

a) Obscrve that there are two possible moves from the point E Q,x 0,a cither to the left or to the right. Hence C +1 p( h ph+1 )h (1 p)(h p(h1 1 h+ 2. 1 - -T As ho 0 a-1 a-1 P h1 -h4) 1a- 1 p ha 1-p For i 1 a-1 1-D 1 -p ha h a-1 1-p As h h11 1 1-p P 1-p 1 1-p h1 P P 1-p 1-p 1-p 1 1 1-p 1-p 1 1

b) We can use the following code to get a simulation for h_x

N 10 h-[0]; for x-1:N p- 0 n x for M-1:100 while x !N n nsign(randn); if n N p p+1 break; end; if n 0 break; end; end; h(x) p/M; end; end;