Andrey Markov

Andrey Andreyevich Markov (1856–1922) was a Russian mathematician who developed the theory of stochastic processes now known as Markov chains.

Markov chain: A stochastic process in which the next state depends on the current state, not the full past. This mathematical structure bears Markov’s name and grew from his work on dependent events.
St. Petersburg State University: A Russian public research university founded in 1724 and based in Saint Petersburg. Markov studied and taught at this university, where his mathematical career took shape.
Stochastic process: A collection of random variables indexed by time or another parameter. Markov chains are one particular kind of stochastic process.
Alexander Lyapunov: A Russian mathematician known for foundational work on stability and probability theory. Lyapunov and Markov were colleagues whose work shaped Russian probability.
Eugene Onegin: A verse novel by Alexander Pushkin, written in Russian and published in full in 1833. Markov counted features of its text to illustrate statistical dependence between successive letters.
Markov property: The condition that a process’s future, given its present, is independent of its earlier history. This memory condition captures the defining feature of the processes Markov studied.
Pafnuty Chebyshev: A Russian mathematician known for work in probability, number theory, and approximation theory. Chebyshev taught Markov and helped establish the probability tradition in which he worked.
Conditional probability: The probability of an event given that another event has occurred. Transition probabilities describe the next state conditional on the present one.
Alexander Pushkin: A Russian poet and writer widely regarded as a founder of modern Russian literature. Markov used the letter patterns in Pushkin’s Eugene Onegin as data for studying dependent sequences.
Markov chain (text generation): A text-generation method that predicts each next unit from a limited preceding context using estimated probabilities. This later application echoes Markov’s use of literary sequences to model transitions.

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