Averaged stochastic processes and
Kolmogorov operators
Pignotti, Michele <1990>
Subject
MAT/06 Probabilità e Statistica matematica
Description
In this thesis we study a class of multidimensional stochastic processes in
which a component is the time integral of another. Our interest stems both
from the great variety of applications and the challenging structure of the
related Kolmogorov backward operators. In fact, while such processes are
widely used in physics and finance, the natural geometric framework to study
them is considerably far from the standard Euclidean one and still vague. We
wish to clarify it developing a new notion of Hölder spaces of any order and
proving a Taylor type formula for functions on them. As applications, we
prove an error estimate for an asymptotic expansion arising in studying Asian
financial options and we also present and analytically investigate a new model
for mine valuation.
Pignotti, Michele (2018) Averaged stochastic processes and Kolmogorov operators, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica , 30 Ciclo. DOI 10.6092/unibo/amsdottorato/8569.