3. Let G =]0, 12. Design and implement an algorithm for the visualization of the harmonic measure on JG for any initial

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3 Let G 0 12 Design And Implement An Algorithm For The Visualization Of The Harmonic Measure On Jg For Any Initial 1 (33.81 KiB) Viewed 28 times

3. Let G =]0, 12. Design and implement an algorithm for the visualization of the harmonic measure on JG for any initial value x € G and to solve the corresponding Dirichlet problem. 4. a) Consider a d-dimensional random vector X whose distribution is symmetric with respect to μ€ Rd, and a function f: Rd → R such that f(X) is square-integrable. Show that 0² (Y)</0² (Y) → Cov(f(X), f(2μ-X)) <0 for Y = f(X) and Ỹ = fg (X). b) Suppose that d = 1. Show that o²(Ỹ) <0²(Y), if ƒ is strictly monotone.