32 citations · 115 across the 22 of their papers we have counts for
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math.PR2014★ 22 cited
A practical criterion for positivity of transition densities
David P. Herzog, Jonathan C. Mattingly
We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion satisfies…
math.PR2014★ 1 cited
Noise-Induced Stabilization of Planar Flows I
David P. Herzog, Jonathan C. Mattingly
We show that the complex-valued ODE \begin{equation*} \dot z_t = a_{n+1} z^{n+1} + a_n z^n+\cdots+a_0, \end{equation*} which necessarily has trajectories along which the dynamics b…
math.PR2014
Noise-Induced Stabilization of Planar Flows II
David P. Herzog, Jonathan C. Mattingly
We continue the work started in Part I of this article, showing how the addition of noise can stabilize an otherwise unstable system. The analysis makes use of nearly optimal Lyapu…