Electronic Communications in Probability

Fill's Algorithm for Absolutely Continuous Stochastically Monotone Kernels

Motoya Machida

Full-text: Open access


Fill, Machida, Murdoch, and Rosenthal (2000) presented their algorithm and its variants to extend the perfect sampling algorithm of Fill (1998) to chains on continuous state spaces. We consider their algorithm for absolutely continuous stochastically monotone kernels, and show the correctness of the algorithm under a set of certain regularity conditions. These conditions succeed in relaxing the previously known hypotheses sufficient for their algorithm to apply.

Article information

Electron. Commun. Probab., Volume 7 (2002), paper no. 15, 141-155.

Accepted: 5 August 2002
First available in Project Euclid: 16 May 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 68U20: Simulation [See also 65Cxx]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 65C05: Monte Carlo methods 65C10: Random number generation 65C40: Computational Markov chains

Markov chain Monte Carlo Fill's algorithm perfect sampling exact sampling rejection sampling stochastic monotonicity partially ordered set monotone coupling absolutely continuous Markov kernel regularity conditions

This work is licensed under aCreative Commons Attribution 3.0 License.


Machida, Motoya. Fill's Algorithm for Absolutely Continuous Stochastically Monotone Kernels. Electron. Commun. Probab. 7 (2002), paper no. 15, 141--155. doi:10.1214/ECP.v7-1056. https://projecteuclid.org/euclid.ecp/1463434782

Export citation


  • Fill. J. A. (1998). An interruptible algorithm for perfect sampling via Markov chains. Ann. Appl. Probab. 8, 131-162.
  • Fill, J. A. and Machida, M. (2001). Stochastic monotonicity and realizable monotonicity. Ann. Probab. 29, 938-978.
  • Fill, J. A., Machida, M., Murdoch, D. J. and Rosenthal, J. S. (2000). Extension of Fill's perfect rejection sampling algorithm to general chains. Random Structures and Algorithms 17, 290-316.
  • Dudley, R. M. (1989). Real Analysis and Probability. Wadsworth and Brooks/Cole, Pacific Grove, California.
  • Folland, G. B. (1984). Real Analysis, 2nd ed. John Wiley & Sons, New York.
  • Kamae, T., Krengel, U., and O'Brien, G. L. (1977). Stochastic inequalities on partially ordered state spaces. Ann. Probab. 5, 899-912.
  • Lindvall, T. (1992). Lectures on the Coupling Method. John Wiley & Sons, New York.
  • Møller, J. and Schladitz, K. (1999). Extensions of Fill's algorithm for perfect simulation. Journal of the Royal Statistical Society, Series B 61, 955-969.
  • Murdoch, D. J. and Green, P. J. (1998). Exact sampling from a continuous state space. Scandinavian Journal of Statistics 25 483-502.
  • Nachbin, L. (1965). Topology and Order. Van Nostrand, New York.
  • Ross, S. (1994). A First Course in Probability, 6th ed. Macmillan, New York.
  • Thöonnes, E. (1999). Perfect simulation of some point processes for the impatient user. Advances in Applied Probability 31, 69-87.