3 papers
math.PR2019
Mean-Field Neural ODEs via Relaxed Optimal Control
Jean-François Jabir, David Šiška, Łukasz Szpruch
We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connection…
math.PR2019
Weak Existence and Uniqueness for McKean-Vlasov SDEs with Common Noise
William R. P. Hammersley, David Šiška, Łukasz Szpruch
This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The i…
math.PR2018
McKean-Vlasov SDEs under Measure Dependent Lyapunov Conditions
William Hammersley, David Šiška, Lukasz Szpruch
We prove the existence of weak solutions to McKean-Vlasov SDEs defined on a domain with continuous and unbounded coefficients that satisfy Lyapunov type…