Dynamical Large Deviations of Reflected Diffusions

In this talk I discuss the calculation of the large deviation functions characterizing the fluctuations of dynamical observables of Markov diffusions with reflecting boundaries. In practice, these large deviation functions are often found via a spectral calculation. The proper boundary conditions for this spectral calculation in the presence of reflecting boundaries is discussed, and the implications for the driven process (which describes how fluctuations arise in the long-time limit) are explored. As an illustration of our results, I will discuss two particular applications (reflected Ornstein-Uhlenbeck process and reflected Brownian motion with drift). Finally, I mention open problems and possible extensions of this work.