Rækkestokastisk

Rækkestokastisk is a Danish term that translates to "row stochastic" in English. It refers to a property of a matrix where the sum of the elements in each row equals one. This type of matrix is fundamental in the study of probability and stochastic processes, particularly in the context of Markov chains.

In a stochastic matrix, each entry $p_{ij}$ represents the probability of transitioning from state $i$ to state $j$. The fact that the sum of each row is one signifies that from any given state, there is a certainty of transitioning to some state, including potentially remaining in the same state. This mathematical property ensures that the probabilities are conserved over time, which is a core requirement for modeling systems that evolve probabilistically.

Rækkestokastiske matrices are widely used in various fields such as finance, biology, physics, and computer science. For example, in a Markov chain model of customer behavior, a rækkestokastisk matrix could describe the probabilities of a customer moving between different purchasing states. The analysis of such matrices allows for predictions about the long-term behavior of the system being modeled. While the term is specific to Danish, the concept it represents is universally understood and applied in probability theory and its applications.