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A Hawkes process is a simple point process whose intensity depends on its history; the resulting dynamics are generally non-Markovian. We establish a sample-path moderate deviation principle for a nonlinear Hawkes process in the full moderate regime. Since a Poisson cluster representation is unavailable for nonlinear H...
This work studies global convergence guarantees of third-order Langevin dynamics for non-convex optimization via simulated annealing with fixed friction and decreasing noise via simulated annealing with fixed friction and decreasing noise.
We study global convergence guarantees of third-order Langevin dynamics for non-convex optimization via simulated annealing with fixed friction and decreasing noise. An explicit three-block distorted entropy transfers dissipation from the noisy auxiliary variable to the full state. Under dissipativity, regularity, and...
We study the underdamped (kinetic) Langevin dynamics confined to a bounded domain $\Omega\subset\mathbb{R}^d$ by specular reflection of the velocity at the boundary. This process is the natural momentum-based analogue of the normally reflected overdamped Langevin diffusion, and it is used in practice for constrained sa...
An explicit quantitative contraction rate is established for HFHR dynamics under a position Poincar\'e inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, where the potential function is not necessarily convex.
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