Recent content by Jimmy Zhan

The attempt at solution: ⟨x, Py⟩ = ⟨Px, y⟩ ∑ixi(Py)πi = ∑i(Px)iyiπi ∑i xi [Py]i πi = ∑i [Px]i yi πi However I don't know what is the form of the P matrix and thus the form of the matrix product Px and Py.

Homework Statement Let X = {Xn : n ≥ 0} be an irreducible, aperiodic Markov chain with finite state space S, transition matrix P, and stationary distribution π. For x,y ∈ R|S|, define the inner product ⟨x,y⟩ = ∑i∈S xiyiπi, and let L2(π) = {x ∈ R|S| : ⟨x,x⟩ < ∞}. Show that X is time-reversible...

Hello, I'm Jimmy. I did my undergrad in Engineering Physics - electrical option at Queen's University, and I'm currently completing my Master of Applied Science in Physics at the same school. My research area is in optics and photonics (solar cells, etc). I am hoping to potentially use this...