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| 確率的動的計画法× | マルコフモデル× | |
|---|---|---|
| 分野 | シミュレーション | シミュレーション |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1957 | 1906 |
| 提唱者≠ | Bellman, R.; formalized for stochastic settings by Puterman, M. L. | Andrei Markov |
| 種類≠ | Sequential optimization under uncertainty | Probabilistic state-transition model |
| 原典≠ | Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093 | Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963 |
| 別名 | SDP, Markov Decision Process, MDP, Stochastic DP | Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process |
| 関連≠ | 6 | 5 |
| 概要≠ | 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. |
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