3 papers
math.PR2026
Weak Convergence of Stochastic Integrals on Skorokhod Space in Skorokhod's J1 and M1 Topologies
Andreas Sojmark, Fabrice Wunderlich
We provide criteria for Itô integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probabil…
math.PR2025
Relative compactness of Itô integrals on the M1 Skorokhod space with identification of limits
Fabrice Wunderlich
We establish general results for weak relative compactness of sequences of Itô integrals with respect to Skorohod's functional M1 topology, under general conditions. Moreover, we…
math.PR2025
Functional weak convergence of stochastic integrals for moving averages and continuous-time random walks
Andreas Søjmark, Fabrice Wunderlich
There is an extensive theory of weak convergence for moving averages and continuous-time random walks (CTRWs) with respect to Skorokhod's M1 and J1 topologies. Here we address the…