We give a mathematical framework for exact milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of exact milestoning and give explicit error bounds for the error in the milestoning equation for mean first passage times.


  1. accelerated molecular dynamics
  2. long-time dynamics
  3. stationary distribution
  4. semi-Markov processes

MSC codes

  1. 82C21
  2. 82C80
  3. 37A30

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Information & Authors


Published In

cover image Multiscale Modeling & Simulation
Multiscale Modeling & Simulation
Pages: 301 - 322
ISSN (online): 1540-3467


Submitted: 14 May 2015
Accepted: 16 December 2015
Published online: 3 March 2016


  1. accelerated molecular dynamics
  2. long-time dynamics
  3. stationary distribution
  4. semi-Markov processes

MSC codes

  1. 82C21
  2. 82C80
  3. 37A30



Funding Information

National Institutes of Health http://dx.doi.org/10.13039/100000002 : GM59796
Division of Mathematical Sciences http://dx.doi.org/10.13039/100000121 : 1522398
Welch Foundation http://dx.doi.org/10.13039/100000928 : F-1783

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