Brownian Motion and Related Models

小行星9700721 从概率论的四个领域的一些问题进行了研究。的 第一，它有偏微分方程的应用，是一个调查， 利用普通布朗运动和迭代布朗运动 议案第二个领域产生于经济学和物理学，是一个随机的领域。 分叉模型一个是常微分方程，它的行为是受控的 一个随机过程。第三个领域是分形上的扩散， 他们的财产。这些都有应用物理以及偏微分方程。 最后，将研究超过程的唯一性，从而应用于 偏微分方程和数学生物学。 概率技术将用于研究一些不同的模型， 出现在经济学、物理学和生物学中。其中包括理性参与者的行为， 经济学、物理学中的场论和生物学中的种群。结果还应 应用于数学中的偏微分方程理论。

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.