Intertwining relations for the first-passage-time problem

D'Onofrio Giuseppe, Politecnico di Torino

We investigate the problem of the first-passage-time through a boundary of some stochastic processes with partial random resetting using the approach of the intertwining between semigroups. Intertwining relations are a type of commutation relations that form a classification scheme for linear operators. Thanks to this strategy some closed form expressions of statistical quantities both for the process itself and for the first-passage-time random variable can be inherited from those known for semigroups of classical processes. Moreover, numerical schemes can be developed. Based on joint works with Pierre Patie (Cornell University), Laura Sacerdote (Università di Torino) and Alessandro Lanteri (Università di Torino).

Area: CS54 - Random motions and first passage times (Alessandra Meoli and Costantino Ricciuti)

Keywords: first passage time, non-local operators, intertwining relations, Markov semigroups, Levy-type processes

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