A random process (see stochastic process) in which the rate of change of a time-dependent quantity ∂a(t)/∂t depends on the instantaneous value of the quantity a(t), where t is the time, but not on its previous history. If a random process can be assumed to be a Markov process, an analysis of the process is greatly simplified enabling many problems in nonequilibrium statistical mechanics and disordered solids to be solved. Problems involving Markov processes are solved using statistical methods and the theory of probability. They are named after the Russian mathematician Andrei Andreevich Markov (1856–1922), who studied such processes in the early years of the 20th century.