Brownian Motion and Related Models

9700721低音要研究概率论四个领域的一些问题。第一个是用普通布朗运动和迭代布朗运动研究拉普拉斯平方的方法，它应用于偏微分方程组。第二个领域源于经济学和物理学，是一个随机分叉模型。我们有一个常微分方程，它的行为是由一个随机过程控制的。第三个领域是分形学上的扩散，以及对其性质的研究。它们在物理学和偏微分方程式中都有应用。最后，我们将研究超过程的唯一性，从而将其应用到偏微分方程和数学生物学中。概率技术将被用来研究经济学、物理学和生物学中出现的一些不同的模型。其中包括经济学中理性参与者的行为，物理学中的场论，以及生物学中的种群。这些结果也应该应用于数学中的偏微分方程组理论。

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.