The Fluid Limit Approximation with Random Initial Conditions for Small Noise Processes

The classical results tell us that the effects of small noise in a smooth dynamical system is negligible on any finite time interval, also known as the fluid limit approximation. This thesis studies situations when it persists on time intervals increasing to infinity, resulting in new random initial conditions appearing in the fluid limit. This has applications in many fields of research, e.g. biology, physics and chemistry, where there are examples of large dynamical systems that arise from small random interactions between many components.