Markovkedjemodeller

Markovkedjemodeller, often simply referred to as Markov models, are mathematical systems that transition from one state to another based on probabilistic rules. The key characteristic of a Markov chain is its "memoryless" property, also known as the Markov property. This means that the probability of transitioning to any future state depends only on the current state and not on the sequence of states that preceded it. In essence, the past history is irrelevant given the present.

These models are defined by a set of states and a transition matrix. The states represent the possible conditions or situations the system can be in, while the transition matrix specifies the probability of moving from one state to another within a single time step. For example, in a weather model, states could be "sunny," "cloudy," and "rainy," and the transition matrix would detail the likelihood of going from "sunny" today to "rainy" tomorrow.

Markovkedjemodeller find wide applications across various fields. In natural language processing, they are used for tasks like predicting the next word in a sentence or generating text. In finance, they can model stock price movements or credit risk. Biology employs them for analyzing DNA sequences or population dynamics. Computer science utilizes them for algorithm design and performance analysis. Their simplicity and probabilistic nature make them powerful tools for understanding and predicting the behavior of complex systems when the Markov property holds.