Concentration inequalities for stochastic differential equations of pure non-Poissonian jumps

Abstract
We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes. (C) 2020 Elsevier B.V. All rights reserved.
Anno
2020
Tipo pubblicazione
Altri Autori
Torrisi, Giovanni Luca
Editore
North-Holland Publ. Co.
Rivista
Stochastic processes and their applications