9700721 Bass A number of problems from four areas of probability theory are to be studied. The first, which has applications to partial differential equations, is an investigation into the squared Laplacian by means of both ordinary Brownian motion and by iterated Brownian motion. The second area arises out of both economics and physics and is a stochastic bifurcation model. One has an ordinary differential equation whose behavior is controlled by a stochastic process. The third area is diffusions on fractals, together with a study of their properties. These have applications to physics as well as partial differential equations. Finally, uniqueness for superprocesses will be investigated, resulting in applications to partial differential equations and to mathematical biology. Probabilistic techniques will be used to study a number of different models that arise in economics, physics, and biology. These include the behavior of rational players in economics, field theories in physics, and populations in biology. The results should also have applications to the theory of partial differential equations in mathematics.
