1 citations · 3 across the 13 of their papers we have counts for
13 papers
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 function…
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 r…
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…
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…
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…
Robustness of Optimal Controlled Diffusions with Near-Brownian Noise via Rough Paths Theory
Somnath Pradhan, Zachary Selk, Serdar Yüksel
In this article we show a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion. Often, Brownian motion is used as an idea…
Rough Paths above Weierstrass Functions
Francesco Cellarosi, Zachary Selk
Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that…
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…
Banach Intermediate Spaces for Gaussian Fréchet Spaces
Yifei Zheng, Zachary Selk
In this article, we show that every centered Gaussian measure on an infinite dimensional separable Fréchet space over admits some full measure Banach intermediate s…
A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions
Zachary Selk, Harsha Honnappa
In this article, we prove a Feynman-Kac type result for a broad class of second order ordinary differential equations. The classical Feynman-Kac theorem says that the solution to a…
Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments
Zachary Selk
In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove la…
Information Projection on Banach spaces with Applications to State Independent KL-Weighted Optimal Control
Zachary Selk, William Haskell, Harsha Honnappa
This paper studies constrained information projections on Banach spaces with respect to a Gaussian reference measure. Specifically our interest lies in characterizing projections o…
Convergence of trapezoid rule to rough integrals
Yanghui Liu, Zachary Selk, Samy Tindel
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals which are not semimartingales and whose -variation is fini…