Ergodicity, mixing dan exactness pada operator Markov

SUTRISNO, Agus, Dr. Widodo, MS

2004 | Tesis | S2 Matematika

Dalam thesis ini akan diperlihatkan kekonvergenan rata-rata barisan {A f } n . Sifat konvergensi maupun prekompak barisan {A f } n , dapat digunakan untuk menunjukkan keberadaan fungsi densitas stasioner. Syarat-syarat konstriktif (constrictive) operator Markov menjamin adanya suatu densitas stasioner * f . Selanjutnya dengan menggunakan sifat kekonstriktifan operator Markov dapat ditunjukkan ergodicity, mixing dan exactness pada operator Markov. Kata kunci : operator Markov, constrictive, ergodicity, mixing dan exactness.

This thesis contains the convergence of sequence averages {A f } n . Convergence and precompact properties of {A f } n that can be applied to show that density stationer function exists. Constrictive conditions of Markov operator guarantees existence of stationer density function * f . Furthermore, by using constrictiveness of Markov operator we will show the ergodicity, mixing and exactness properties of Markov operator. Key words : Markov operator, constrictive, ergodicity, mixing and exactness 1

Kata Kunci : Matematika,Operator Markov,Ergodicity, Mixing dan Exactness