Markov

Markov is a surname of Slavic origin and is associated with several figures in science and literature. In mathematics and probability theory, it most commonly refers to Andrey Andreyevich Markov (1856–1922), a Russian mathematician who founded the theory of Markov chains. His work introduced the idea that the future state of a random process depends only on its present state, not on the sequence of events that preceded it—a memoryless property now known as the Markov property.

Markov chains are stochastic processes that move between a finite or countable set of states in discrete time steps or in continuous time. In a discrete-time Markov chain, the probability of transitioning to a new state depends only on the current state, described by a transition matrix. Continuous-time Markov chains use rates of transition between states. Key topics within Markov chain theory include stationary distributions, convergence to equilibrium, and conditions for recurrence.

Applications of Markov methods span many disciplines, including physics, economics, linguistics, genetics, and computer science. Hidden Markov models combine Markovian state progression with observable outputs and are widely used in areas such as speech recognition and bioinformatics. The Markov framework also underpins various Monte Carlo techniques, notably Markov chain Monte Carlo, which uses a Markov process to sample from complex probability distributions. The surname Markov appears in diverse contexts beyond mathematics, reflecting its use as a family name in many cultures and its association with notable contributors across fields.