Other Applied Mathematics Commons^™

A New Model For Predicting Probabilities Of Viable Pregnancy And Multiple Gestations For I̲N̲ V̲I̲T̲R̲O̲ Fertilization, Ray Vernon Haning Jr.

Theses, Dissertations and Capstones

In vitro fertilization (IVF) can be viewed as high stakes gambling with more than one winning outcome and more than one outcome leading to failure. Knowing the odds of successful outcomes, the odds of outcomes leading to failure, and the various costs is a tremendous asset in any form of gambling. Four important variables have been reported to affect pregnancy rates in IVF programs: age of patient, number of unsuccessful prior attempts, embryo morphology, and number of embryos transferred.

While it is desirable to optimize pregnancy rates, such optimization may often result in a high incidence of multiple gestation. Data …

On Optimal Ergodic Control Of Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an optimal ergodic control problem where the state of the system is given by a diffusion process with jumps in the whole space. The corresponding dynamic programming (or Hamilton-Jacobi-Bellman) equation is a quasi-linear integro-differential equation of second order. A key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only locally bounded and Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic HJB equation is established.