- A characterisation of isometries with respect to the Lévy-Prokhorov metric(arXiv)
Writer : György Pál Gehér, Tamás Titkos
Summary : In line with the elemental work of Yu.V. Prokhorov, the final concept of stochastic processes will be thought to be the idea of chance measures in full separable metric areas. Since stochastic processes relying upon a steady parameter are mainly chance measures on sure subspaces of the area of all features of an actual variable, a very essential case of this concept is when the underlying metric area has a linear construction. Prokhorov additionally supplied a concrete metrisation of the topology of weak convergence immediately often called the L{é}vy-Prokhorov distance. Motivated by these information, the well-known Banach-Stone theorem, and a few latest works associated to characterisations of onto isometries of areas of Borel chance measures, right here we give an entire description of surjective isometries with respect to the L{é}vy-Prokhorov metric in case when the underlying metric area is a separable Banach area. Our end result will be thought of as a generalisation of L. Molnár’s earlier Banach-Stone-type end result which characterises onto isometries of the area of all chance distribution features on the actual line wit respect to the Lévy distance. Nevertheless, the current extra basic setting requires the event of an primarily new techniqu
