Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Selk, Zachary"'
Autor:
Cellarosi, Francesco, Selk, Zachary
In this paper, we study the stochastic calculus for the theta process. The theta process is a stochastic process of number theoretical origin arising as a scaling limit of quadratic Weyl sums. It has several properties in common with Brownian motion
Externí odkaz:
http://arxiv.org/abs/2406.05523
Autor:
Selk, Zachary, Yüksel, Serdar
Decentralized stochastic control problems with local information involve problems where multiple agents and subsystems which are coupled via dynamics and/or cost are present. Typically, however, the dynamics of such couplings is complex and difficult
Externí odkaz:
http://arxiv.org/abs/2405.20498
Autor:
Mansouri, Abdol-Reza, Selk, Zachary
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 note we give a stochastic representation for solutions of hyperbolic PDE.
Externí odkaz:
http://arxiv.org/abs/2401.08848
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 idealized model of a diffusion where approximations such as Wong-Zakai, Ka
Externí odkaz:
http://arxiv.org/abs/2310.09967
Autor:
Cellarosi, Francesco, Selk, Zachary
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 if one can define "iterated integrals" above a signal, then one can c
Externí odkaz:
http://arxiv.org/abs/2304.11646
The Small-Noise Limit of the Most Likely Element is the Most Likely Element in the Small-Noise Limit
Autor:
Selk, Zachary, Honnappa, Harsha
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 measures. The Onsager-Machlup function can serve as a density on infinite d
Externí odkaz:
http://arxiv.org/abs/2209.04523
Autor:
Zheng, Yifei, Selk, Zachary
In this article, we show that every centered Gaussian measure on an infinite dimensional separable Fr\'{e}chet space $X$ over $\mathbb R$ admits some full measure Banach intermediate space between $X$ and its Cameron-Martin space. We provide a way of
Externí odkaz:
http://arxiv.org/abs/2107.09440
Autor:
Selk, Zachary, Honnappa, Harsha
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 broad class of second order parabolic equations is the mean of a part
Externí odkaz:
http://arxiv.org/abs/2106.08525
Autor:
Selk, Zachary
Publikováno v:
Statistics and Probability Letters 206 (C). March 2024
In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such processes on inte
Externí odkaz:
http://arxiv.org/abs/2103.04501
This paper studies constrained information projections on Banach spaces with respect to a Gaussian reference measure. Specifically our interest lies in characterizing projections of the reference measure, with respect to the KL-divergence, onto sets
Externí odkaz:
http://arxiv.org/abs/2009.03504