3 papers
math.PR2026
Tightness criteria for random compact sets of cadlag paths
Nic Freeman, Jan M. Swart
We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This…
math.GN2025
Skorokhod's topologies on path space
Nic Freeman, Jan M. Swart
Skorokhod's J1 and M1 topologies are standard tools in proving limit theorems for stochastic processes. Motivated by applications, we extend these topologies so that they are capab…
math.DS2025
Böttcher-type potential for the secant map
Nicholas Freeman
We present a construction of a Böttcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the Böttcher-typ…