Übergangsquoten

Übergangsquoten, often translated as transition rates or transition probabilities, are a fundamental concept in various fields, including statistics, physics, and economics. They represent the likelihood or probability that a system will move from one state to another within a given period. In essence, they quantify the dynamism of a system by describing how it changes over time.

In the context of Markov chains, Übergangsquoten are represented by a transition matrix. Each entry in this matrix, denoted as $P_{ij}$, signifies the probability of transitioning from state $i$ to state $j$ in a single step. The sum of probabilities across each row of the transition matrix must equal one, as the system is guaranteed to transition to some state.

The applications of Übergangsquoten are diverse. In physics, they are used to model the behavior of particles, such as in radioactive decay where the transition rate from an unstable state to a stable state is a key parameter. In economics, they can describe consumer behavior, credit risk assessment, or the movement of individuals between different employment statuses. Understanding these rates is crucial for predicting future states, analyzing system stability, and making informed decisions.