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In probability theory and statistics, a Markov chain or Markoff chain, named after the Russian mathematician Andrey Markov, is a stochastic process that satisfies the Markov property (usually characterized as "memorylessness"). Loosely speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history. i.e., conditional on the present state of the system, its future and past are independent.[1] In discrete time, the process is known as a discrete-time Markov chain (DTMC[2]). It undergoes transitions from one state to another on a state space, with the probability distribution of the next state depending only on the current state and not on the sequence of events that preceded it. In continuous time, the process is known as a Continuous-time Markov chain (CTMC[1] or continuous-time Markov process[2]). It takes values in some state space and the time spent in each state takes non-negative real values and has an exponential distribution. Future behaviour of the model (both remaining time in current state and next state) depends only on the current state of the model and not on historical behaviour.

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確率論および統計、マルコフ連鎖またはマルコフ チェーン、ロシアの数学者アンドレイ ・ マルコフ (通常は"memorylessness"として特徴付けられる) マルコフ性を満たす確率過程後に名前付き。大まかに言えば、プロセスのためのマルコフ性を満たすベース プロセスの未来予測できる場合

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Probability theory and statistics, Markov chain or Markov and Markov chains, the Russia mathematician Andrey Markov (typically characterized as "memorylessness") to meet the probability process after named. Broadly speaking, meet with the Markov process for base process

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確率論と統計、マルコフ連鎖マルコフやマルコフ チェーン、ロシアの数学者アンドレイ ・ マルコフ (通常の特徴は"memorylessness") という後の確率過程を満たすために。大まかに言えば、基本プロセスにおけるマルコフ過程と会う

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Statistics and probability theory, Markov chain Markov and Markov chains, the Russia mathematician Andrey Markov (usually feature "memorylessness") that meet the probability process of the after. Broadly speaking, see Markov process base

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統計と確率理論、マルコフ連鎖マルコフ、マルコフ チェーン、ロシアの数学者アンドレイ ・ マルコフ (通常機能"memorylessness") の確率過程に合った、後。大まかに言えば、マルコフ参照してくださいプロセス ベース

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Stochastic theory of statistics and probability theory, Markov chain Markov and Markov chains, the Russia mathematician Andrey Markov (usually feature "memorylessness"), after. Broadly speaking, Markov, see process-based

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統計と確率理論、マルコフ連鎖マルコフ、マルコフ連鎖、ロシアの数学者アンドレイ ・ マルコフ (通常機能「memorylessness」)、の確率過程論後。大まかに言えば、マルコフ プロセス ベースを参照してください。

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Statistics and probability theory, Markov chain Markov and Markov, Russia mathematician Andrey Markov (usually feature "memorklessness"), the probability theory then. Broadly speaking, see Markov process-based.

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統計と確率論、マルコフ連鎖マルコフ ・ マルコフ、ロシアの数学者アンドレイ ・ マルコフ (通常機能"memorklessness")、確率論。大まかに言えば、マルコフ プロセス ベースを参照してください。

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Statistics and probability theory, Markov chain Markov and Markov, Russia mathematician Andrey Markov (usually feature "memorklessness"), and probability theory. Broadly speaking, see Markov process-based.

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統計と確率論、確率論のマルコフ連鎖マルコフ ・ マルコフ、ロシア数学者アンドレイ ・ マルコフ (通常機能"memorklessness")、大まかに言えば、マルコフ プロセス ベースを参照してください。

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Statistics and probability theory, stochastic Markov chain Markov and Markov, Russia mathematician Andrey Markov (usually feature "memorklessness"), broadly speaking, see Markov process-based.

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統計と確率論、確率論的マルコフ連鎖マルコフ ・ マルコフ、ロシアの数学者アンドレイ ・ マルコフ (通常機能"memorklessness")、大まかに言えば、マルコフ プロセス ベースを参照してください。

BACK INTO ENGLISH

Statistics and probability theory, stochastic Markov chain Markov and Markov, Russia mathematician Andrey Markov (usually feature "memorklessness"), broadly speaking, see Markov process-based.