Linganisha mbinu

	Mfumo wa Markov	Mfumo wa Markov wa Kistokastiki
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1906	1993
Mwanzilishi	Andrei Markov	Markov, A. A. (probabilistic extension developed by Sonnenberg & Beck and others)
Aina	Probabilistic state-transition model	Probabilistic state-transition model with Monte Carlo uncertainty propagation
Chanzo asilia	Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963	Sonnenberg, F. A., & Beck, J. R. (1993). Markov models in medical decision making: A practical guide. Medical Decision Making, 13(4), 322–338.
Majina mbadala	Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process	Probabilistic Markov Model, Stochastic Markov Chain, SMM, Monte Carlo Markov Model
Zinazohusiana	5	6
Muhtasari	A Markov Model represents a system as a finite set of states and specifies the probability of moving from one state to another at each time step. By capturing only the current state — not the full history — it enables tractable analysis of complex dynamic processes across health economics, engineering reliability, operations research, and social-science modeling.	A Stochastic Markov Model is a simulation technique that represents a system as a set of mutually exclusive health or decision states, moves a cohort (or individual agents) through those states using probabilistically sampled transition parameters, and aggregates outcomes across thousands of Monte Carlo iterations to produce full probability distributions over costs, outcomes, or rankings rather than single point estimates.