Upcoming seminars

Abstract: The topic of the presentation is the connection between the Large Deviation Principle (LDP) for the invariant measure of a random process and the LDP for the same process in the space of trajectories. It is shown that if the trajectory action functional has a certain structure and the family of invariant measures is exponentially tight, then the LDP for invariant measures follows from the trajectory LDP, regardless of other properties of the random process. The action functional for the invariant measure is characterized in terms of the solution to the max-balance equations, which arise as a limit in the sense of large deviations of the equilibrium equations for the invariant measure. The non-uniqueness of the equilibrium position of the corresponding dynamic system is allowed. As an application, the LDP for the invariant measure of a diffusion process with jumps is considered.