Asymptotic results for a class of Markovian self-exciting processes

Spectra of some self - exciting and mutually exciting point processes

In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a, b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum ...

Explicit results for wear processes in a Markovian environment

We consider the reliability of a single-unit system whose cumulative damage over time is a continuous wear process {X (t): t¿ 0} that depends on an external environment process {Z(t): t¿ 0}. We explicitly derive the failure time distribution and moments in terms of Laplace–Stieltjes transforms by analyzing the Markov additive process {(X (t); Z(t)): t¿ 0} and demonstrate its applicability on an...

Ergodic properties of a class of non-Markovian processes

We study a fairly general class of time-homogeneous stochastic evolutions driven by noises that are not white in time. As a consequence, the resulting processes do not have the Markov property. In this setting, we obtain constructive criteria for the uniqueness of stationary solutions that are very close in spirit to the existing criteria for Markov processes. In the case of discrete time, wher...

Asymptotic Properties and Optimization of Some Non-Markovian Stochastic Processes

Jǐŕı Anděl, Sergej Čelikovský, Marie Demlová, Jan Flusser, Petr Hájek, Vladimı́r Havlena, Didier Henrion, Yiguang Hong, Zdeněk Hurák, Martin Janžura, Jan Ježek, George Klir, Ivan Kramosil, Tomáš Kroupa, Petr Lachout, Friedrich Liese, Jean-Jacques Loiseau, Frantǐsek Matúš, Radko Mesiar, Karol Mikula, Jǐŕı Outrata, Jan Seidler, Karel Sladký Jan Štecha, Olga Štěpánková, Frantǐsek Turnovec, Igor Vaj...

Self-exciting point processes with applications in finance and medicine