Research Projects

The principal objective of the proposed research is to study limit theorems for switching Markov processes in the presence of multiple spatial and/or temporal scales. We are particularly interested in using homogenization techniques to understand the large scale long time behavior of switching diffusion processes with spatially periodic coefficients and jump intensities. This study is motivated by, but by no means limited to, mathematical models of molecular motors: specialized molecules like kinesin and dynein in the interiors of biological cells which transport cellular organelles across the spatial expanse of the cell by "walking" along tracks with periodic structure. The mathematical novelty of the proposed research is the extension of well-known homogenization techniques for diffusions to the case of switching diffusions. In addition, the theoretical results obtained can be expected to provide analytically simpler and computationally cheaper tools to understand certain subcellular phenomena of scientific interest.