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Long‐Time Behaviour of Langevin Algorithms with Time‐dependent Energy Function
Author(s) -
Grillo Gabriele
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951720111
Subject(s) - pointwise , mathematics , langevin dynamics , function (biology) , distribution (mathematics) , energy (signal processing) , langevin equation , statistical physics , distribution function , mathematical analysis , mathematical physics , physics , statistics , quantum mechanics , evolutionary biology , biology
We study the Langevin algorithm on C ∞ n ‐dimensional compact connected Riemannian manifolds and on IR n , allowing the energy function U to vary with time. We find conditions under which the distribution of the process at hand becomes indistinguishable as t → ∞ from the “instantaneous” equilibrium distribution. Such conditions do not necessarily imply that U(t ) converges pointwise as t → ∞.