Affiliation:
1. Dipartimento di Matematica , Università “Tor Vergata” , via della Ricerca Scientifica , Rome , Italy
Abstract
Abstract
We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If X(t) is a one-dimensional diffusion with jumps, starting from a random position η ∈ [a, b], let be τ
a,b the time at which X(t) first exits the interval (a, b), and π
a = P (X(τ
a,b) ≤ a) the probability of exit from the left of (a, b). Given a probability q ∈ (0, 1), the problem consists in finding the density g of η (if it exists) such that π
a = q; it can be seen as a problem of optimization.
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