قارن الطرق

	البرمجة الديناميكية العشوائية	نموذج ماركوف
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1957	1906
صاحب الطريقة	Bellman, R.; formalized for stochastic settings by Puterman, M. L.	Andrei Markov
النوع	Sequential optimization under uncertainty	Probabilistic state-transition model
المصدر التأسيسي	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093	Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963
الأسماء البديلة	SDP, Markov Decision Process, MDP, Stochastic DP	Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process
ذات صلة	6	5
الملخص	Stochastic Dynamic Programming (SDP) is a mathematical optimization framework for sequential decision problems where outcomes are partly random. It extends Bellman's principle of optimality to stochastic environments, representing problems as Markov Decision Processes (MDPs) and computing optimal policies by solving recursive value equations over states and time periods.	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.