Stochastic Processes
نویسنده
چکیده
x 6∈S cxf(x) 2 < ε. Of course g has finite support since g(x) = 0 for x 6∈ S. u t Exercise 2. (*) Recall that the operator norm of an operator T : U → W is define ||T || = supu 6=0 {||Tu||/||u||}. Show the following: • The transition matrix P is a self-adjoint operator from L(V ) into itself. • The operator norm of P is at most 1. • ||P|| ≤ ||P ||. • ||P || = ||P ||. Solution (exercise 2). Since P = I −∆ and ∆ : L(V )→ L(V ) then also P : L(V )→ L(V ). Also, 〈Pf, g〉 = ∑
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