Abstract. We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann . Our study was prompted by some concrete problems in battery modelling , and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass-Lyons , and then Bailleul, Catellier and Delarue . Such a "pathwise McKean-Vlasov theory" can be traced back to Tanaka . This paper can be seen as an attempt to advertize the ideas, power and simplicity of the pathwise appproach, not so easily extracted from [4, 10, 40], together with a number of novel applications. These include mean field convergence without a priori independence and exchangeability assumption; common noise, càdlàg noise, and reflecting boundaries. Last not least, we generalize Dawson-Gärtner large deviations and the central limit theorem to a non-Brownian noise setting.
Pathwise McKean-Vlasov Theory with Additive Noise / M. Coghi, J. Deuschel, P. Friz, M. Maurelli. - (2018 Dec 31).
|Titolo:||Pathwise McKean-Vlasov Theory with Additive Noise|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2018-12-31|
|Appare nelle tipologie:||24 - Pre-print|