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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:

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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.

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