My current research interests include stochastic analysis, functional analysis, and applications to economic theory.
PapersFatou limits of stochastic integrals
V. Melnikov. Fatou limits of stochastic integrals (preprint).
Risk measures on incomplete markets: a new non-solid paradigm
V. Melnikov. Risk measures on incomplete markets: a new non-solid paradigm (preprint).
Limit theorems for \(\sigma\)-localized Émery convergence
V. Melnikov. Limit theorems for \(\sigma\)-localized Émery convergence. Journal of Theoretical Probability 38:1 (2025).
Relative weak compactness in infinite-dimensional Fefferman-Meyer duality
V. Melnikov. Relative weak compactness in infinite-dimensional Fefferman-Meyer duality. Journal of Mathematical Analysis and Applications 543:1 (2025).
On \(\mathfrak{L}_{\infty}\)-liftings of the Gelfand-Naimark morphism
V. Melnikov. On \(\mathfrak{L}_{\infty}\)-liftings of the Gelfand-Naimark morphism. Matematicheskie Zametki 115:6 (2024), 914-918.
Finding a limit of a bounded sequence of semimartingales
20th Oxford-Berlin Young Researchers Meeting on Applied Stochastic Analysis (December 10, 2024). Mathematical Institute, University of Oxford.