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Mark J.
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How to mathematically proof that an arrival process is Markov ,memory-less ?
Mark J. said:The process is people arrival at the bus stop.
I have time arrivals and now I need to proof that is indeed markovian process and maybe poisson
A Markov Memory-less Process is a type of stochastic process where the future states of the system depend only on the current state, not on any previous states. This means that the system has no memory of its past states and only the current state matters in predicting future states.
To prove that a process is Markov Memory-less, we need to show that the conditional probability of the future states only depends on the current state and is independent of any previous states. This can be done using mathematical equations and proofs, such as the Chapman-Kolmogorov Equations or the Markov Property.
Proofing Markov Memory-less Processes mathematically is important because it allows us to understand and analyze the behavior of these systems with certainty. It also helps in making predictions and decisions based on the current state of the system, which can be useful in various fields such as finance, engineering, and biology.
Markov Memory-less Processes have many real-world applications, including stock market analysis, weather forecasting, speech recognition, and DNA sequence analysis. They are also commonly used in machine learning and artificial intelligence algorithms.
Yes, a process can be both Markov and Memory-less. In fact, all Markov processes are Memory-less by definition. However, not all Memory-less processes are Markov, as they may still have dependencies on past states that affect future states. It is important to distinguish between Markov and Memory-less processes when analyzing and modeling systems.