6 papers
On the Onsager-Machlup functional of the -measure
Ioannis Gasteratos, Zachary Selk
We investigate the existence of generalised densities for the measures, in finite volume, through the lens of Onsager-Machlup (OM) functionals. The latter are…
Reweighting metric measure spaces and Onsager-Machlup
Zachary Selk
Given a metric measure space the Onsager-Machlup (OM) functional is a real valued function that has been seen as a generalized notion of a probability density functio…
Stochastic Calculus for the Theta Process
Francesco Cellarosi, Zachary Selk
The theta process is a stochastic process of number theoretical origin arising as a scaling limit of quadratic Weyl sums. It can be described in terms of the geodesic flow and an a…
Stochastic Solutions for Hyperbolic PDE
Abdol-Reza Mansouri, Zachary Selk
The theory of stochastic representations of solutions to elliptic and parabolic PDE has been extensive. However, the theory for hyperbolic PDE is notably lacking. In this short not…
Robust Decentralized Control of Coupled Systems via Risk Sensitive Control of Decoupled or Simple Models with Measure Change
Zachary Selk, Serdar Yüksel
Decentralized stochastic control problems with local information involve problems where multiple agents and subsystems which are coupled via dynamics and/or cost are present. Typic…
The Small-Noise Limit of the Most Likely Element is the Most Likely Element in the Small-Noise Limit
Zachary Selk, Harsha Honnappa
In this paper, we study the Onsager-Machlup function and its relationship to the Freidlin-Wentzell function for measures equivalent to arbitrary infinite dimensional Gaussian measu…