.png){kind=icon}
.png){kind=icon}
Return
Weak convergence of stochastic integrals on Skorokhod space in Skorokhod's J1 and M1 topologies
.png){kind=icon}
PRE
AI
S
W
DOI：10.1007/s00440-026-01476-y.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We provide criteria for It & ocirc; integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probability. The results are novel in the M1 setting and unify existing theories in the J1 case. Beyond sufficient criteria, we present an example of uniformly convergent martingale integrators for which the continuity breaks down. Moreover, we show that, for families of local martingales, M1 tightness in fact implies J1 tightness under a mild localised uniform integrability condition. Finally, we apply our results to study scaling limits of models of anomalous diffusion driven by continuous-time random walks. This yields new results on weak M1 and J1 convergence to stochastic integrals against subordinated stable processes. In the case of superdiffusive scaling, an interesting counterexample is obtained.
Keywords:
TIME RANDOM-WALKS
MEAN-FIELD GAMES
LIMIT-THEOREMS
DRIVEN
Journal
P
IF:
1.6
Papers:
61
Citations:
0
Organization
Cited Papers