- AutorIn
- Bernd Hofmann
- Titel
- On multiplication operators occurring in inverse problems of natural sciences and stochastic finance
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:swb:ch1-200501261
- Erschienen in
- Tagungsband zum Workshop "Stochastische Analysis", 27.09.2004 - 29.09.2004
- Abstract (EN)
- We deal with locally ill-posed nonlinear operator equations F(x) = y in L^2(0,1), where the Fréchet derivatives A = F'(x_0) of the nonlinear forward operator F are compact linear integral operators A = M ◦ J with a multiplication operator M with integrable multiplier function m and with the simple integration operator J. In particular, we give examples of nonlinear inverse problems in natural sciences and stochastic finance that can be written in such a form with linearizations that contain multiplication operators. Moreover, we consider the corresponding ill-posed linear operator equations Ax = y and their degree of ill-posedness. In particular, we discuss the fact that the noncompact multiplication operator M has only a restricted influence on this degree of ill-posedness even if m has essential zeros of various order.
- Freie Schlagwörter
- Fréchet derivative
- ill-posedness
- inverse problem
- multiplication operator
- option pricing
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- Inverses Problem
- Multiplikationsoperator
- Publizierende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:swb:ch1-200501261
- Veröffentlichungsdatum Qucosa
- 07.10.2005
- Dokumenttyp
- Vorlesung/Vortrag
- Sprache des Dokumentes
- Englisch