3 Added references edit approved Sep 3 '13 at 15:28 Comp_Warrior 1,4951515 silver badges3535 bronze badges Overview A Markov process is any stochastic process $$Y_{t}$$ such that the future is conditionally independent of the past, given the present; the distribution of the process only depends on where the process is, not where it has been: $$P(Y_{t+1}=y_{t+1} |Y_t = y_{t}, Y_{t-1} = y_{t-1}, ..., Y_{1} = y_{1}) = P(Y_{t+1}=y_{t+1} |Y_t = y_{t})$$ This property is known as the Markov property. References The following threads on math.se provide references to resources on Markov processes: A Markov process is any stochastic process $$Y_{t}$$ such that the future is conditionally independent of the past, given the present; the distribution of the process only depends on where the process is, not where it has been: $$P(Y_{t+1}=y_{t+1} |Y_t = y_{t}, Y_{t-1} = y_{t-1}, ..., Y_{1} = y_{1}) = P(Y_{t+1}=y_{t+1} |Y_t = y_{t})$$ This property is known as the Markov property. Overview A Markov process is any stochastic process $$Y_{t}$$ such that the future is conditionally independent of the past, given the present; the distribution of the process only depends on where the process is, not where it has been: $$P(Y_{t+1}=y_{t+1} |Y_t = y_{t}, Y_{t-1} = y_{t-1}, ..., Y_{1} = y_{1}) = P(Y_{t+1}=y_{t+1} |Y_t = y_{t})$$ This property is known as the Markov property. References The following threads on math.se provide references to resources on Markov processes: 2 Simplified excerpt; moved details to tag wiki edit approved Aug 30 '13 at 10:22 Comp_Warrior 1,4951515 silver badges3535 bronze badges A Markov process is any stochastic process $$Y_{t}$$ such that the future is conditionally independent of the past, given the present; the distribution of the process only depends on where the process is, not where it has been: $$P(Y_{t+1}=y_{t+1} |Y_t = y_{t}, Y_{t-1} = y_{t-1}, ..., Y_{1} = y_{1}) = P(Y_{t+1}=y_{t+1} |Y_t = y_{t})$$ This property is known as the Markov property. A Markov process is any stochastic process $$Y_{t}$$ such that the future is conditionally independent of the past, given the present; the distribution of the process only depends on where the process is, not where it has been: $$P(Y_{t+1}=y_{t+1} |Y_t = y_{t}, Y_{t-1} = y_{t-1}, ..., Y_{1} = y_{1}) = P(Y_{t+1}=y_{t+1} |Y_t = y_{t})$$ This property is known as the Markov property. 1 | link created May 22 '12 at 0:30