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5 papers · 2 filters
A note on intermittency for the fractional heat equation
Raluca Balan, Daniel Conus
The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-Δ)^{β/2} u(t,x) + u(t,x…
A Compensator Characterization of Planar Point Processes
B. Gail Ivanoff
Martingale techniques play a fundamental role in the analysis of point processes on the real line. In particular, the compensator of a point process uniquely determines and is dete…
Integration with respect to Lévy colored noise, with applications to SPDEs
Raluca Balan
In this article, we introduce a Lévy analogue of the spatially homogeneous Gaussian noise of Dalang (1999), and we construct a stochastic integral with respect to this noise. The s…
Scaling Properties of Paths on Graphs
R. Edwards, E. Foxall, T. J. Perkins
Let be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on . Fix vertices and and consider the set of paths that start…
Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements
Aaron Smith
Let and be two Markov chains, on state spaces . In this paper, we discuss how to prove bounds on the spectrum of based on bounds on the spec…