Convergence to global minima for a class of diffusion processes

Jianfeng Feng, Hans-Otto Georgii and David Brown

Physica A: Statistical Mechanics and its Applications, 2000, vol. 276, issue 3, 465-476

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.

Keywords: Simulated annealing; Robbins–Monro procedures; Kiefer–Wolfowitz procedures; Gain function (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:276:y:2000:i:3:p:465-476

DOI: 10.1016/S0378-4371(99)00486-0

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