Edwin K P Chong

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We consider stochastic approximation algorithms on a general Hilbert space, and study four conditions on noise sequences for their analysis: Kushner and Clark's condition, Chen's condition, a decomposition condition, and Kulkarni and Horn's condition. We discuss various properties of these conditions. In our main result we s h o w that the four conditions(More)
We describe a method for the analysis of the distribution of displacements, i.e., the propagators, of single-particle tracking measurements for the case of obstructed subdiffusion in two-dimensional membranes. The propagator for the percolation cluster is compared with a two-component mobility model against Monte Carlo simulations. To account for diffusion(More)
1745 " hysteresis, " caused by the subcritical bifurcation. The bifurcation diagrams for the backstepping controller (57) are shown in Fig. 4 for c 0 = 6 and 2 k = 0:5. This controller " softens " the bifurcation from subcritical to supercritical and eliminates the hysteresis. In addition, it stabilizes all stall equilibria and prevents surge for all values(More)
1745 " hysteresis, " caused by the subcritical bifurcation. The bifurcation diagrams for the backstepping controller (57) are shown in Fig. 4 for c 0 = 6 and 2 k = 0:5. This controller " softens " the bifurcation from subcritical to supercritical and eliminates the hysteresis. In addition, it stabilizes all stall equilibria and prevents surge for all values(More)
We develop deterministic necessary and sufficient conditions on individual noise sequences of a stochastic approximation algorithm for the error of the iterates to converge at a given rate. Specifically, suppose {p,} is a given positive sequence converging monotonically to 0. Consider a stochastic approximation algorithm x,+1 = x,-an(Anxn-b,) + anen, where(More)
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