10,184 research outputs found
Numerical study of ergodicity for the overdamped Generalized Langevin Equation with fractional noise
The Generalized Langevin Equation, in history, arises as a natural fix for
the rather traditional Langevin equation when the random force is no longer
memoryless. It has been proved that with fractional Gaussian noise (fGn) mostly
considered by biologists, the overdamped Generalized Langevin equation
satisfying fluctuation-dissipation theorem can be written as a fractional
stochastic differential equation (FSDE). While the ergodicity is clear for
linear forces, it remains less transparent for nonlinear forces. In this work,
we present both a direct and a fast algorithm respectively to this FSDE model.
The strong orders of convergence are proved for both schemes, where the role of
the memory effects can be clearly observed. We verify the convergence theorems
using linear forces, and then present the ergodicity study of the double well
potentials in both 1D and 2D setups
An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems
Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust
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