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Full-Text Articles in Probability

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk Sep 1993

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …


Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi Jan 1993

Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi

Mathematics Faculty Research Publications

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.


Studies Of Electron-Beam Penetration And Free-Carrier Generation In Diamond Films, R. P. Joshi, K. H. Schoenbach, C. Molina, W. W. Hofer Jan 1993

Studies Of Electron-Beam Penetration And Free-Carrier Generation In Diamond Films, R. P. Joshi, K. H. Schoenbach, C. Molina, W. W. Hofer

Bioelectrics Publications

Experimental observations of the energy‐dependent electron‐beam penetration in type II‐A natural diamond are reported. The experimental data are compared with results obtained from numerical Monte Carlo simulations, and the results are in very good agreement. The results also reveal that a threshold energy of about 125 keV is necessary for complete penetration for a 35 μm sample. It is found that over the 30–180 keV range, the energy dependence of the penetration depth and total path length exhibits a power‐law relation. Monte Carlo simulations have also been performed to investigate the excess carrier‐generation profiles within diamond for a set of …