Mathematics of Errors
portes grátis
Mathematics of Errors
Bouleau, Nicolas
Springer Nature Switzerland AG
02/2022
448
Dura
Inglês
9783030885748
15 a 20 dias
821
Descrição não disponível.
I. Error computations a la Gauss.- 1. The different approaches.- 2. Finite dimensional examples.- 3. An intuitive introduction to error structures.- 4. Weakly and strongly random errors.- II. Probabilistic and Functional Models.- 5. Strongly continuous semi-groups and Dirichlet forms.- 6. Error structures.- 7. Images and products of error structures.- 8. The gradient and the sharp and other calculation tools.- 9. Error structures on fundamental spaces.- III. The subtleness of the notion of bias.- 10. Approximation and bias operators.- 11. Computations and simulation methods.- IV. Error structures and its applications.- 12. Statistical identification of error structures.- 13. The instantaneous structure of a stochastic process.- 14. Models inspired by finance.- 15. Examples in Physics.- 16. The principle of arbitrary functions and error structures.- V. Historical elements and research themes.- 17. Error calculations from Gauss and Laplace.- 18. Extensions and open questions.- Hints for exercises.- Pedagogical References.- Chronological Bibliography.
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Ornstein-Uhlenbeck;error structures;square field operator;stochastic differential equation;variance of error;bias of error;Malliavin calculus;Mathematical Finance;Quantitative Finance
I. Error computations a la Gauss.- 1. The different approaches.- 2. Finite dimensional examples.- 3. An intuitive introduction to error structures.- 4. Weakly and strongly random errors.- II. Probabilistic and Functional Models.- 5. Strongly continuous semi-groups and Dirichlet forms.- 6. Error structures.- 7. Images and products of error structures.- 8. The gradient and the sharp and other calculation tools.- 9. Error structures on fundamental spaces.- III. The subtleness of the notion of bias.- 10. Approximation and bias operators.- 11. Computations and simulation methods.- IV. Error structures and its applications.- 12. Statistical identification of error structures.- 13. The instantaneous structure of a stochastic process.- 14. Models inspired by finance.- 15. Examples in Physics.- 16. The principle of arbitrary functions and error structures.- V. Historical elements and research themes.- 17. Error calculations from Gauss and Laplace.- 18. Extensions and open questions.- Hints for exercises.- Pedagogical References.- Chronological Bibliography.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
