állapotúMarkovlánc

állapotúMarkovlánc is a mathematical system that transitions from one state to another on a state space. The probability of transitioning to any particular state depends solely on the current state and not on the sequence of events that preceded it. This property is known as the Markov property or "memorylessness". The states can be discrete or continuous, and the transitions occur over discrete or continuous time. A common representation of an állapotúMarkovlánc is through a transition matrix, where each entry represents the probability of moving from one state to another. The rows of this matrix sum to one, indicating that from any given state, there's a certainty of transitioning to some state. These models are widely used in various fields, including physics, economics, biology, and computer science, to model phenomena exhibiting such memoryless behavior. Examples include modeling the weather, stock price movements, or the spread of diseases. The analysis of állapotúMarkovlánc often involves studying concepts like stationary distributions, which describe the long-term probabilities of being in each state, and the convergence of the system to these distributions.