4 papers
Convergence, Sticking and Escape: Stochastic Dynamics Near Critical Points in SGD
Dmitry Dudukalov, Artem Logachov, Vladimir Lotov +3
We study the convergence properties and escape dynamics of Stochastic Gradient Descent (SGD) in one-dimensional landscapes, separately considering infinite- and finite-variance noi…
Moments of the first descending epoch for a random walk with negative drift
Sergey Foss, Timofej Prasolov
We consider the first exit time from the positive halfline of a random walk with i.d.d. summands having a negative drif…
Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons
Timofei Prasolov
We study a system of perfect integrate-and-fire inhibitory neurons. It is a system of stochastic processes which interact through receiving an instantaneous increase at the moments…
Limit theorems and structural properties of the Cat-and-Mouse Markov chain
Timofei Prasolov, Sergey Foss, Seva Shneer
We revisit the so-called Cat-and-Mouse Markov chain, studied earlier by Litvak and Robert (2012). This is a 2-dimensional Markov chain on the lattice , where the firs…