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Convergence to global minima for a class of diffusion processes

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  • Feng, Jianfeng
  • Georgii, Hans-Otto
  • Brown, David

Abstract

We prove that there exists a gain function (η(t),β(t))t⩾0 such that the solution of the SDE dxt=η(t)(−gradU(xt)dt+β(t)dBt) ‘settles’ down on the set of global minima of U. In particular, the existence of a gain function (η(t))t⩾0 so that yt satisfying dyt=η(t)(−gradU(yt)dt+dBt) converges to the set of the global minima of U is verified. Then we apply the results to the Robbins–Monro and the Kiefer–Wolfowitz procedures which are of particular interest in statistics.

Suggested Citation

  • Feng, Jianfeng & Georgii, Hans-Otto & Brown, David, 2000. "Convergence to global minima for a class of diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(3), pages 465-476.
    • Handle: RePEc:eee:phsmap:v:276:y:2000:i:3:p:465-476
    DOI: 10.1016/S0378-4371(99)00486-0
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    References listed on IDEAS

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    1. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
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    Cited by:

    1. Chen, Neiping & Liu, Wenbin & Feng, Jianfeng, 2006. "Sufficient and necessary condition for the convergence of stochastic approximation algorithms," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 203-210, January.

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