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We study the convergence behavior of the stochastic heavy-ball method with a small stepsize.
Morse Lemma
J. Milnor · 1963
Earlier work this paper cites.
Some methods of speeding up the convergence of iteration methods
B.T. Polyak · 1964
Earlier work this paper cites.
Functional Analysis
K. Yosida · 1965
Earlier work this paper cites.
The exit problem for small random perturbations of dynamical systems with a hyperbolic fixed point
Y. Kifer · 1981
Earlier work this paper cites.
Geometric Methods in the Theory of Ordinary Differential Equations, Grundlehren der mathematischen Wissenschaften, 250
V.I. Arnold · 1988
Earlier work this paper cites.
On the exit law from saddle points
M.V. Day · 1995
Earlier work this paper cites.
Introduction to the modern theory of dynamical systems, Encyclopaedia of Mathematics and its Applications, Vol 54
A. Katok and B. Hasselblatt · 1995
Earlier work this paper cites.
Random perturbations of nonlinear oscillators
M. Freidlin and M. Weber · 1998
Earlier work this paper cites.
Asymptotic behavior of the first exit time of randomly perturbed dynamical systems with a repulsive equilibrium point
T. Mikami · 1998
Earlier work this paper cites.
On stochastic behavior in perturbed Hamiltonian systems
M. Brin and M. Freidlin · 2000
Earlier work this paper cites.
On random perturbations of Hamiltonian systems with many degrees of freedom
M. Freidlin and M. Weber · 2001
Earlier work this paper cites.
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