What does the Markov Property refer to in stochastic processes?

The Markov Property is fundamentally defined as the memoryless property in stochastic processes. This means that the future state of a system depends only on its present state and not on the sequence of events that preceded it. In other words, given the current state, the next state is conditionally independent of all prior states. This property simplifies the analysis of complex systems, allowing them to be modeled more easily and efficiently.

This characteristic is particularly important in various applications, including Markov Chains and decision-making processes in AI, where understanding current states can lead to predictable future states without needing to track all previous states.

The other options, while they may touch on concepts related to state transitions or dependencies in different contexts, do not directly define what the Markov Property signifies. For example, memory retention capability suggests a historical influence on future states, which contradicts the memoryless aspect. Long-term dependency involves influences from past states over time, again conflicting with the Markovian assumption. Markov Chain behavior relates specifically to the implementation of the Markov Property in a structured manner but does not encapsulate the core concept itself.