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Convergence to Global Minima for a Class of Diffusion Processes
- Handbook of research on teaching (3rd ed
, 2000
"... We prove that there exists a gain function (#(t);#(t)) t0 such that the solution of the SDE dx t =#(t)(-grad U (x t )dt+#(t)dB t ) `settles' down on the set of global minima of U . In particular, the existence of a gain function (#(t)) t0 so that y t satisfying dy =#(t)(-grad U (y t )dt+dB t ) conve ..."
Abstract
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We prove that there exists a gain function (#(t);#(t)) t0 such that the solution of the SDE dx t =#(t)(-grad U (x t )dt+#(t)dB t ) `settles' down on the set of global minima of U . In particular, the existence of a gain function (#(t)) t0 so that y t satisfying dy =#(t)(-grad U (y t )dt+dB t ) 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.
