Markov process

Named after Russian mathematician Andrey Markov (Андре́й Андре́евич Ма́рков) (1856—1922), who researched the processes.

Markov process (plural Markov processes)

1. (probability theory) Any stochastic process for which the conditional probability distribution of future states depends only on the current state (and not on past states).
   • 2007, N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd Edition, page 81,

     It has been remarked in 1 that a Markov process with time reversal is again a Markov process.

   • 2009, Yuri Kifer, Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging, Memoirs of the American Mathematical Society, Number 944, page vii,

     The second part is written for probabilists and it studies the case where fast motions are certain Markov processes such as random evolutions and, in particular, diffusions.

   • 2013, M. G. Shur, Markov Process, entry in Michiel Hazewinkel (editor), Encyclopaedia of Mathematics, Volume 6, page 102,

     In the theory of Markov processes most attention is given to homogeneous (in time) processes.

• Markov chain

• Markov renewal process
• semi-Markov process

• Markovian

• Markov model
• Markov property
• memoryless