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1 1 It is well-known that, for a continuous-time Markov process, the transition probabilities $mathbf{P} = mathbb{P}left[X(t) = j |X(0) = iright]$ satisfy the following evolution equation: $$frac{dmathbf{P}}{dt} = mathbf{A}{mathbf{P}}$$ where $mathbf{A}$ is a time-independent matrix usually called the generator matrix. If I were to identify a stochastic process whose transition probabilities evolve according to this equation, would this immediately imply the process possesses the Markov property? probability stochastic-processes markov-process share | cite | improve this question edited 2 days ago aghostinthefig

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