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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 sharp general conditions. Moreover…
Functional CLTs for subordinated Lévy models in physics, finance, and econometrics
Andreas Søjmark, Fabrice Wunderlich
We present a simple unifying treatment of a broad class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where (possibly s…
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…
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 probabili…
Asymptotic strong Feller property and local weak irreducibility via generalized couplings
Oleg Butkovsky, Fabrice Wunderlich
In this short note we show how the asymptotic strong Feller property (ASF) and local weak irreducibility can be established via generalized couplings. We also prove that a stronger…