On positively divisible non-Markovian processes

Canturk B., Breuer H.

Journal of Physics A: Mathematical and Theoretical, cilt.57, sa.26, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 26
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1088/1751-8121/ad5525
  • Dergi Adı: Journal of Physics A: Mathematical and Theoretical
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Chapman-Kolmogorov equation, Kolmogorov consistency conditions, non-Markovian stochastic processes, P-divisibility
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process to be classified as a stochastic process. Combining the Kolmogorov consistency conditions with the Chapman-Kolmogorov equation, we derive a necessary condition for positively divisible stochastic processes on a finite sample space. This necessary condition enables a systematic approach to the manipulation of certain Markov processes in order to obtain a positively divisible non-Markovian process. We illustrate this idea by an example and, in addition, analyze a classic example given by Feller in the light of our approach.