Systems of equations driven by fast-oscillating functions of a Wiener process
Mathematical Physics and Probability Seminar
Several applied problems lead to systems of differential equations in the plane, where random terms appear with singular coefficients. Examples are motion of a light-sensitive robot in an inhomogeneous environment and a model of motility-induced phase separation (MIPS). We studied singular limits of these systems obtained by (nonrigorous) singular perturbation theory and found some puzzling phenomena: the system with only one noise source converges (in law) to a system driven by two independent noises and the singular limit acquires an additional drift term which does not correspond to any term in the original equation. I will report on a general theorem which covers the applications mentioned above and much more, explaining the structure of the limiting equations. The work has been done jointly with Tanner Reese as a part of his RTG project. The paper containing the results has been submitted to arXiv.