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Error calculus for finance and physics : the language of Dirichlet forms / / by Nicolas Bouleau



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Autore: Bouleau Nicolas Visualizza persona
Titolo: Error calculus for finance and physics : the language of Dirichlet forms / / by Nicolas Bouleau Visualizza cluster
Pubblicazione: Berlin ; ; New York, : Walter de Gruyter, c2003
Edizione: 1st ed.
Descrizione fisica: 1 online resource (244 p.)
Disciplina: 511/.43
Soggetto topico: Error analysis (Mathematics)
Dirichlet forms
Random variables
Classificazione: SK 820
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- Contents -- Chapter I Intuitive introduction to error structures -- Chapter II Strongly-continuous semigroups and Dirichlet forms -- Chapter III Error structures -- Chapter IV Images and products of error structures -- Chapter V Sensitivity analysis and error calculus -- Chapter VI Error structures on fundamental spaces space -- Chapter VII Application to financial models -- Chapter VIII Applications in the field of physics -- Back matter
Sommario/riassunto: Many recent advances in modelling within the applied sciences and engineering have focused on the increasing importance of sensitivity analyses. For a given physical, financial or environmental model, increased emphasis is now placed on assessing the consequences of changes in model outputs that result from small changes or errors in both the hypotheses and parameters. The approach proposed in this book is entirely new and features two main characteristics. Even when extremely small, errors possess biases and variances. The methods presented here are able, thanks to a specific differential calculus, to provide information about the correlation between errors in different parameters of the model, as well as information about the biases introduced by non-linearity. The approach makes use of very powerful mathematical tools (Dirichlet forms), which allow one to deal with errors in infinite dimensional spaces, such as spaces of functions or stochastic processes. The method is therefore applicable to non-elementary models along the lines of those encountered in modern physics and finance. This text has been drawn from presentations of research done over the past ten years and that is still ongoing. The work was presented in conjunction with a course taught jointly at the Universities of Paris 1 and Paris 6. The book is intended for students, researchers and engineers with good knowledge in probability theory.
Titolo autorizzato: Error calculus for finance and physics  Visualizza cluster
ISBN: 1-282-19475-5
9786612194757
3-11-019929-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910819012703321
Lo trovi qui: Univ. Federico II
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Serie: Gruyter expositions in mathematics ; ; 37.