AIP conference proceedings

Non-Markovian stochastic processes

Daniel T. Gillespie

Published Jan 1, 2000• 3 citations

Abstract

New perspectives on non-Markovian stochastic process theory are provided by recent work on the question of whether quantum mechanical measurement statistics can be modeled as a self-consistent stochastic process.

DOI: 10.1063/1.60002

Related papers

Quantum mechanics can be formulated as a non-Markovian stochastic process

German A. Skorobogatov, Sergey Igorevich Svertilov

Both quantum mechanics and stochastic-process theory deal with dynamical systems the behaviors of which can be predicted only probabilistically. It is shown here that the measurable behavior of an elementary quantum system can be modeled as a non-Markovian stochastic process. The conclusion that quantum behavior can generally be modeled as a real stochastic process eliminates some mysterious characteristics of quantum mechanics when viewed in Copenhagen-interpretation terms.

Physical Review ANov 1, 199816 citations

Quantum mechanics as a theory of non-Markov random processes

Vladimir Dmitriev

SPhDFeb 1, 19870 citations

Non-Markovian quantum stochastic processes and their entropy

Göran Lindblad

Communications in Mathematical PhysicsOct 1, 1979122 citations

Is quantum mechanics equivalent to a classical stochastic process?

Hermann Grabert, Peter Hänggi A, Peter Talkner A

The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.

Physical Review AJun 1, 197981 citations

Description of quantum-mechanical motion by using the formalism of non-Markov stochastic processes

German A. Skorobogatov, Sergei I. Svertilov

PANFeb 1, 19990 citations

Stochastic and numerical approaches to dissipative quantum dynamics: path integrals and beyond

Jürgen T. Stockburger

Abstract Recent advances using non‐Markovian stochastic techniques in the treatment of system–reservoir models of quantum dissipation are reviewed, outlining their derivation from the influence functional formalism and discussing their new features and potential applications. A coherent perspective of the salient features in the mathematical foundations of dissipative quantum mechanics, diverse established perturbative and numerical methods, and more recent non‐Markovian stochastic approaches is attempted.

physica status solidi (b)Apr 24, 20039 citations