Some stability results of parameter identification in a jump diffusion model

• Main Author: Düvelmeyer, Dana
• Language: English
• Published: Technische Universität Chemnitz 2005
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; Inverses Problem; Stabilität; Jump diffusion; compact domain; ill-posedness; parameter identification; stability
• Online Access: http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501234; https://monarch.qucosa.de/id/qucosa%3A18372; https://monarch.qucosa.de/api/qucosa%3A18372/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A18372/attachment/ATT-1/

In this paper we discuss the stable solvability of the inverse problem of parameter identification in a jump diffusion model. Therefore we introduce the forward operator of this inverse problem and analyze its properties. We show continuity of the forward operator and stability of the inverse problem provided that the domain is restricted in a specific manner such that techniques of compact sets can be exploited. Furthermore, we show that there is an asymptotical non-injectivity which causes instability problems whenever the jump intensity increases and the jump heights decay simultaneously.