Efficiency of Parallel and Restart Exploration Strategies in Model-Free Stochastic Simulations

Published Online:https://doi.org/10.1287/stsy.2025.0108

References

  • Asmussen S, Glynn PW (2007) Stochastic Simulation: Algorithms and Analysis, Stochastic Modelling and Applied Probability, vol. 57 (Springer, New York).Google Scholar
  • Asselah A, Ferrari PA, Groisman P (2011) Quasistationary distributions and Fleming-Viot processes in finite spaces. J. Appl. Probab. 48(2):322–332.Google Scholar
  • Avrachenkov K, Piunovskiy A, Zhang Y (2018) Hitting times in Markov chains with restart and their application to network centrality. Methodology Comput. Appl. Probab. 20(4):1173–1188.Google Scholar
  • Bertoin J (1998) Lévy Processes, Cambridge Tracts in Mathematics, vol. 121 (Cambridge University Press, Cambridge, UK).Google Scholar
  • Bertoin J, Doney RA (1994) Cramér’s estimate for Lévy processes. Statist. Probab. Lett. 21(5):363–365.Google Scholar
  • Borovkov A (2013) Probability Theory (Springer, London).Google Scholar
  • Budhiraja A, Fraiman N, Waterbury A (2022) Approximating quasi-stationary distributions with interacting reinforced random walks. ESAIM Probab. Statist. 26:69–125.Google Scholar
  • Burdzy K, Hołyst R, Ingerman D, March P (1996) Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions. J. Phys. A Math. General 29(11):2633–2642.Google Scholar
  • Collet P, Martínez S, San Martín J (2013) Quasi-stationary Distributions., Markov Chains, Diffusions and Dynamical Systems (Springer, Berlin).Google Scholar
  • Denisov D, Shneer V (2013) Asymptotics for the first passage times of Lévy processes and random walks. J. Appl. Probab. 50(1):64–84.Google Scholar
  • Doney RA (1985) Conditional limit theorems for asymptotically stable random walks. Zeitschrift Wahrscheinlichkeitstheor. Verwandte Gebiete 70:351–360.Google Scholar
  • Doney RA, Maller RA (2004) Moments of passage times for Lévy processes. Ann. Inst. Henri Poincaré Probab. Statist. 40(3):279–297.Google Scholar
  • Ecoffet A, Huizinga J, Lehman J, Stanley KO, Clune J (2021) First return, then explore. Nature 590:580–586.Google Scholar
  • Evans MR, Majumdar SN, Schehr G (2020) Stochastic resetting and applications. J. Phys. A Math. Theoret. 53(19):193001.Google Scholar
  • Ferrari PA, Marić N (2007) Quasi stationary distributions and Fleming-Viot processes in countable spaces. Electronic J. Probab. 12:684–702.Google Scholar
  • Grigorescu I, Kang M (2013) Markov processes with redistribution. Markov Processes Related Fields 19(3):497–520.Google Scholar
  • Hansen NR (2009) The maximum of a Lévy process reflected at a general barrier. Stochastic Processes Appl. 119(7):2336–2356.Google Scholar
  • Höglund T (1990) An asymptotic expression for the probability of ruin within finite time. Ann. Probab. 18(1):378–389.Google Scholar
  • Iglehart DL (1974) Random walks with negative drift conditioned to stay positive. J. Appl. Probab. 11(4):742–751.Google Scholar
  • Kolb M, Savov M (2014) Exponential ergodicity of killed Lévy processes in a finite interval. Electronic Comm. Probab. 19:1–9.Google Scholar
  • Kyprianou AE (2006) Introductory Lectures on Fluctuations of Lévy Processes with Applications (Springer, Berlin).Google Scholar
  • Kyprianou AE (2014) Fluctuations of Lévy Processes with Applications, Introductory Lectures, 2nd ed. (Springer, Berlin).Google Scholar
  • Kyprianou AE, Palmowski Z (2006) Quasi-stationary distributions for Lévy processes. Bernoulli 12(4):571–581.Google Scholar
  • Lambert A (2000) Completely asymmetric Lévy processes confined in a finite interval. Ann. Inst. Henri Poincaré Probab. Statist. 36(2):251–274.Google Scholar
  • Luby M, Sinclair A, Zuckerman D (1993) Optimal speedup of Las Vegas algorithms. Inform. Processing Lett. 47(4):173–180.Google Scholar
  • Martinez S, San Martin J (1994) Quasi-stationary distributions for a Brownian motion with drift and associated limit laws. J. Appl. Probab. 31(4):911–920. Google Scholar
  • Mastropietro D, Ayesta U, Jonckheere M, Majewski S (2025) Fast-exploring reinforcement learning with applications to stochastic networks. Queueing Systems 109(3):23.Google Scholar
  • Méléard S, Villemonais D (2012) Quasi-stationary distributions and population processes. Probab. Surveys 9:340–410.Google Scholar
  • Monthus C (2021) Large deviations for Markov processes with stochastic resetting: Analysis via the empirical density and flows or via excursions between resets. J. Statist. Mech. Theory Experiment 2021(3):033201.Google Scholar
  • Palmowski Z, Pistorius M (2009) Cramér asymptotics for finite time first passage probabilities of general Lévy processes. Statist. Probab. Lett. 79(16):1752–1758.Google Scholar
  • Villemonais D (2011) Interacting particle systems and Yaglom limit approximation of diffusions with unbounded drift. Electronic J. Probab. 16:1663–1692.Google Scholar
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