How can I write the following 2D Random Walks command in Matlab? Can anyone help me?
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Two-Dimensional Random Walks: Let x(t) and y(t) be two independent random walks with the same parameters s and T.
(a) Simulate the vector-valued random process (x(t), y(t)) and plot a few sample functions when s = T = 1.
(b) For each sample function you generate in part (a), estimate the mean value of the process by computing a time average. Compare it against the theoretical value of E{(x(t), y(t))} and explain any discrepancies you might discover.
(c) Let r(t) = (x 2 (t)+y 2 (t)) 1 / 2 denote the radial distance of the walk from the origin. Show that for t ≫ T and r on the order of (αt) 1 / 2 , where α = s 2 /T, that the first order density function is
f(r, t) ≈r/αt exp ( −r^2/2αt) U(r).
(d) Verify the claim in part (c) by simulation.
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