Invariant Distribution

• If g is the PDF. T(x|y) is the PDF of the transition kernel. Homogenous Markov Chain. Then g is PDF of an invariant distribution of T(x|y) if
• $g(x)={\int }_{{\mathbb{R}}^k}T(x|y)g(y)dy$
• Atleast one invariant distribution
• Ergodic