Stochastic integration with jumps:
Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some nov...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2002
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 89 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical engineering and finance who need to use stochastic differential equations |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiii, 501 pages) |
| ISBN: | 9780511549878 |
| DOI: | 10.1017/CBO9780511549878 |
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| 505 | 8 | 0 | |t Motivation: Stochastic Differential Equations |t Wiener Process |t The General Model |t Integrators and Martingales |t The Elementary Stochastic Integral |t The Semivariations |t Path Regularity of Integrators |t Processes of Finite Variation |t Martingales |t Extension of the Integral |t The Daniell Mean |t The Integration Theory of a Mean |t Countable Additivity in p-Mean |t Measurability |t Predictable and Previsible Processes |t Special Properties of Daniell's Mean |t The Indefinite Integral |t Functions of Integrators |t Ito's Formula |t Random Measures |t Control of Integral and Integrator |t Change of Measure--Factorization |t Martingale Inequalities |t The Doob-Meyer Decomposition |t Semimartingales |t Previsible Control of Integrators |t Levy Processes |t Stochastic Differential Equations |t Existence and Uniqueness of the Solution |t Stability: Differentiability in Parameters |t Pathwise Computation of the Solution |t Weak Solutions |t Stochastic Flows |t Semigroups, Markov Processes, and PDE |t Complements to Topology and Measure Theory |t Notations and Conventions |t Topological Miscellanea |t Measure and Integration |t Weak Convergence of Measures |t Analytic Sets and Capacity |t Suslin Spaces and Tightness of Measures |t The Skorohod Topology |t The L[superscript p]-Spaces |t Semigroups of Operators |
| 520 | |a Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical engineering and finance who need to use stochastic differential equations | ||
| 650 | 4 | |a Stochastic integrals | |
| 650 | 4 | |a Jump processes | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Bichteler, Klaus |
| author_facet | Bichteler, Klaus |
| author_role | aut |
| author_sort | Bichteler, Klaus |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV043942046 |
| classification_rvk | SK 430 SK 820 |
| collection | ZDB-20-CBO |
| contents | Motivation: Stochastic Differential Equations Wiener Process The General Model Integrators and Martingales The Elementary Stochastic Integral The Semivariations Path Regularity of Integrators Processes of Finite Variation Martingales Extension of the Integral The Daniell Mean The Integration Theory of a Mean Countable Additivity in p-Mean Measurability Predictable and Previsible Processes Special Properties of Daniell's Mean The Indefinite Integral Functions of Integrators Ito's Formula Random Measures Control of Integral and Integrator Change of Measure--Factorization Martingale Inequalities The Doob-Meyer Decomposition Semimartingales Previsible Control of Integrators Levy Processes Stochastic Differential Equations Existence and Uniqueness of the Solution Stability: Differentiability in Parameters Pathwise Computation of the Solution Weak Solutions Stochastic Flows Semigroups, Markov Processes, and PDE Complements to Topology and Measure Theory Notations and Conventions Topological Miscellanea Measure and Integration Weak Convergence of Measures Analytic Sets and Capacity Suslin Spaces and Tightness of Measures The Skorohod Topology The L[superscript p]-Spaces Semigroups of Operators |
| ctrlnum | (ZDB-20-CBO)CR9780511549878 (OCoLC)849900810 (DE-599)BVBBV043942046 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511549878 |
| format | Electronic eBook |
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| id | DE-604.BV043942046 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511549878 |
| language | English |
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| publishDate | 2002 |
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| publisher | Cambridge University Press |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Bichteler, Klaus Verfasser aut Stochastic integration with jumps Klaus Bichteler Cambridge Cambridge University Press 2002 1 online resource (xiii, 501 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 89 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Motivation: Stochastic Differential Equations Wiener Process The General Model Integrators and Martingales The Elementary Stochastic Integral The Semivariations Path Regularity of Integrators Processes of Finite Variation Martingales Extension of the Integral The Daniell Mean The Integration Theory of a Mean Countable Additivity in p-Mean Measurability Predictable and Previsible Processes Special Properties of Daniell's Mean The Indefinite Integral Functions of Integrators Ito's Formula Random Measures Control of Integral and Integrator Change of Measure--Factorization Martingale Inequalities The Doob-Meyer Decomposition Semimartingales Previsible Control of Integrators Levy Processes Stochastic Differential Equations Existence and Uniqueness of the Solution Stability: Differentiability in Parameters Pathwise Computation of the Solution Weak Solutions Stochastic Flows Semigroups, Markov Processes, and PDE Complements to Topology and Measure Theory Notations and Conventions Topological Miscellanea Measure and Integration Weak Convergence of Measures Analytic Sets and Capacity Suslin Spaces and Tightness of Measures The Skorohod Topology The L[superscript p]-Spaces Semigroups of Operators Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical engineering and finance who need to use stochastic differential equations Stochastic integrals Jump processes Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-14214-4 Erscheint auch als Druckausgabe 978-0-521-81129-3 https://doi.org/10.1017/CBO9780511549878 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bichteler, Klaus Stochastic integration with jumps Motivation: Stochastic Differential Equations Wiener Process The General Model Integrators and Martingales The Elementary Stochastic Integral The Semivariations Path Regularity of Integrators Processes of Finite Variation Martingales Extension of the Integral The Daniell Mean The Integration Theory of a Mean Countable Additivity in p-Mean Measurability Predictable and Previsible Processes Special Properties of Daniell's Mean The Indefinite Integral Functions of Integrators Ito's Formula Random Measures Control of Integral and Integrator Change of Measure--Factorization Martingale Inequalities The Doob-Meyer Decomposition Semimartingales Previsible Control of Integrators Levy Processes Stochastic Differential Equations Existence and Uniqueness of the Solution Stability: Differentiability in Parameters Pathwise Computation of the Solution Weak Solutions Stochastic Flows Semigroups, Markov Processes, and PDE Complements to Topology and Measure Theory Notations and Conventions Topological Miscellanea Measure and Integration Weak Convergence of Measures Analytic Sets and Capacity Suslin Spaces and Tightness of Measures The Skorohod Topology The L[superscript p]-Spaces Semigroups of Operators Stochastic integrals Jump processes Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4126478-2 |
| title | Stochastic integration with jumps |
| title_alt | Motivation: Stochastic Differential Equations Wiener Process The General Model Integrators and Martingales The Elementary Stochastic Integral The Semivariations Path Regularity of Integrators Processes of Finite Variation Martingales Extension of the Integral The Daniell Mean The Integration Theory of a Mean Countable Additivity in p-Mean Measurability Predictable and Previsible Processes Special Properties of Daniell's Mean The Indefinite Integral Functions of Integrators Ito's Formula Random Measures Control of Integral and Integrator Change of Measure--Factorization Martingale Inequalities The Doob-Meyer Decomposition Semimartingales Previsible Control of Integrators Levy Processes Stochastic Differential Equations Existence and Uniqueness of the Solution Stability: Differentiability in Parameters Pathwise Computation of the Solution Weak Solutions Stochastic Flows Semigroups, Markov Processes, and PDE Complements to Topology and Measure Theory Notations and Conventions Topological Miscellanea Measure and Integration Weak Convergence of Measures Analytic Sets and Capacity Suslin Spaces and Tightness of Measures The Skorohod Topology The L[superscript p]-Spaces Semigroups of Operators |
| title_auth | Stochastic integration with jumps |
| title_exact_search | Stochastic integration with jumps |
| title_full | Stochastic integration with jumps Klaus Bichteler |
| title_fullStr | Stochastic integration with jumps Klaus Bichteler |
| title_full_unstemmed | Stochastic integration with jumps Klaus Bichteler |
| title_short | Stochastic integration with jumps |
| title_sort | stochastic integration with jumps |
| topic | Stochastic integrals Jump processes Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Stochastic integrals Jump processes Stochastisches Integral |
| url | https://doi.org/10.1017/CBO9780511549878 |
| work_keys_str_mv | AT bichtelerklaus stochasticintegrationwithjumps |