övergångssannolikheterna

**Övergångssannolikhet** refers to the probability of transitioning from one state to another in a stochastic process, commonly studied in fields such as probability theory, statistics, and operations research. The concept is central to Markov chains, a type of random process where the future state depends only on the current state and not on the sequence of events that preceded it. In this framework, an **övergångssannolikhet** matrix (or transition probability matrix) is used to represent the likelihood of moving between different states over discrete time intervals.

The values in the matrix are constrained such that each row sums to one, ensuring that the system will always transition to some state. For example, if a Markov chain models weather patterns with states "sunny," "rainy," and "cloudy," the **övergångssannolikhet** from "sunny" to "rainy" might be 0.2, meaning there is a 20% chance of transitioning from sunny to rainy weather in the next time step.

This concept is widely applied in real-world scenarios, such as modeling customer behavior in marketing, predicting stock market trends, or analyzing network traffic patterns. By understanding transition probabilities, analysts can forecast long-term behavior, optimize resource allocation, or make data-driven decisions. The simplicity of Markov chains makes them particularly useful for systems where dependencies on past states are minimal, though more complex models may be required for scenarios with memory or non-stationary transitions.