Modeling and analysis of systems with nonlinear functional dependence on random quantities

Many real-world physical systems exhibit noisy evolution; interpreting their finite-time behavior as arising from continuous-time processes (in the Ito or Stratonovich sense) has led to significant success in modeling and analyzing them. In this talk we explore a class of differential equations where evolution depends nonlinearly on a random or effectively-random quantity, and we argue that these equations may exhibit finite-time stochastic behavior in line with an equivalent Ito process, which is of great utility for their numerical simulation and theoretical analysis. We put forward a method for this conversion, develop an equilibrium-moment relation for Ito attractors, and show that this relation holds for our example nonlinear-converted Ito system. This work enables the theoretical and numerical examination of a wider class of mathematical models which might otherwise be oversimplified due to lack of appropriate tools.