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Doctoral Student presents new results in the area of renewal theory

Ying Ni is a Doctoral Student in Applied mathematics at Mälardalen university. As a result of her research, Ying Ni now presents new results in the area of renewal theory that can be applied to mathematical models like a risk process which models the functioning of an insurance company.

On Friday May 7th, Ying Ni will defend her licentiate thesis called “Perturbed Renewal Equations with Non-Polynomial Perturbations”. In her thesis, Ying Ni investigates the model of perturbed renewal equation with non-polynomial perturbations. Similar models of perturbed renewal equations, where the perturbations are polynomial, have been well studied in the literature, but here she examines non-polynomial type of perturbations, i.e. the renewal equation under consideration depends on some small parameter in a non-polynomial way.

- The purpose of this research is to generalize the renewal theorem to the model of perturbed renewal equations with non-polynomial perturbations, Ying Ni explains. By saying “perturbed renewal equations” we mean that the renewal equations under consideration depend on some small parameter in some sense. This thesis studies the model of perturbed renewal equations with perturbations of a non-polynomial type that has not yet been investigated in the literature.

The theoretical results developed in the thesis can be applied to various areas in applied probability theory. In this thesis, the results are applied to a perturbed risk process which models the functioning of an insurance company. Limit results on the so-called ruin probability for the perturbed risk process have been obtained. These results are not considered as formulas that can be used directly for any field applications, but rather as new, innovative results in the area of risk theory that can later be extended to more complex mathematical models.