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1.

図書

図書
Klaus Bichteler
出版情報: Cambridge : Cambridge University Press, 2002  xiii, 501 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 89
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目次情報: 続きを見る
Preface
Introduction / Chapter 1:
Motivation: Stochastic Differential Equations / 1.1:
Wiener Process / 1.2:
The General Model / 1.3:
Integrators and Martingales / Chapter 2:
The Elementary Stochastic Integral / 2.1:
The Semivariations / 2.2:
Path Regularity of Integrators / 2.3:
Processes of Finite Variation / 2.4:
Martingales / 2.5:
Extension of the Integral / Chapter 3:
The Daniell Mean / 3.1:
The Integration Theory of a Mean / 3.2:
Countable Additivity in p-Mean / 3.3:
Measurability / 3.4:
Predictable and Previsible Processes / 3.5:
Special Properties of Daniell's Mean / 3.6:
The Indefinite Integral / 3.7:
Functions of Integrators / 3.8:
Ito's Formula / 3.9:
Random Measures / 3.10:
Control of Integral and Integrator / Chapter 4:
Change of Measure--Factorization / 4.1:
Martingale Inequalities / 4.2:
The Doob-Meyer Decomposition / 4.3:
Semimartingales / 4.4:
Previsible Control of Integrators / 4.5:
Levy Processes / 4.6:
Stochastic Differential Equations / Chapter 5:
Existence and Uniqueness of the Solution / 5.1:
Stability: Differentiability in Parameters / 5.3:
Pathwise Computation of the Solution / 5.4:
Weak Solutions / 5.5:
Stochastic Flows / 5.6:
Semigroups, Markov Processes, and PDE / 5.7:
Complements to Topology and Measure Theory / Appendix A:
Notations and Conventions / A.1:
Topological Miscellanea / A.2:
Measure and Integration / A.3:
Weak Convergence of Measures / A.4:
Analytic Sets and Capacity / A.5:
Suslin Spaces and Tightness of Measures / A.6:
The Skorohod Topology / A.7:
The L[superscript p]-Spaces / A.8:
Semigroups of Operators / A.9:
Answers to Selected Problems / Appendix B:
References
Index of Notations
Index
Answers
Full Indexes
Errata
Preface
Introduction / Chapter 1:
Motivation: Stochastic Differential Equations / 1.1:
2.

図書

図書
Jun Kigami
出版情報: Providence, R.I. : American Mathematical Society, 2012, c2011  v, 132 p. ; 26 cm
シリーズ名: Memoirs of the American Mathematical Society ; no. 1015
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3.

図書

図書
Rama Cont, Peter Tankov
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2004  xvi, 535 p. ; 25 cm
シリーズ名: Chapman & Hall/CRC financial mathematics series
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目次情報: 続きを見る
Financial Modelling Beyond Brownian Motion
Mathematical Tools
Simulation and Estimation
Option Pricing in Models with Jumps
Beyond Levy Processes
Appendices
Bibliography
Index
Financial Modelling Beyond Brownian Motion
Mathematical Tools
Simulation and Estimation
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