Jabarkan Distiribusi awal nyaéta P(X0). dari Ranté Markov dalam bahasa sunda

Evolusi prosés ngaliwatan sakali tahap waktu nu dijéntrékeun ku

Ieu mangrupa versi Frobenius-Perron equation.

di dinya aya hiji atawa leuwih tetapan distribusi π saperti

nu mana Y ngan sakadar ngaran variabel integrasi.

Saperti distribution π disebut stationary distribution atawa steady-state distribution.

Stationary distribution nyaéta eigenfunction tina fungsi conditional distribution, nu pakait jeung eigenvalue 1.

Whether or not there is a stationary distribution,

and whether or not it is unique if it does exist,

are determined by certain properties of the process.

Irreducible méans that every state is accessible from every other state.

Aperiodic méans that there exists at léast one state for which the transition from that state to itself is possible. Positive recurrent méans that the expected return time is finite for every state.

Sometimes the terms indecomposable, acyclic, and persistent are used as synonyms for "irreducible", "aperiodic", and "recurrent", respectively.

If the Markov chain is positive recurrent,

there exists a stationary distribution.

If it is positive recurrent and irreducible,

there exists a unique stationary distribution,

and furthermore the process constructed by taking the stationary distribution as the initial distribution is ergodic.

Then the average of a function f over samples of the Markov chain is equal to the average with respect to the stationary distribution,