Stability of stochastic differential equations driven by general semimartingales

Słomiński, Leszek

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Stability of stochastic differential equations driven by general semimartingales

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Słomiński Leszek

Seria

Rozprawy Matematyczne tom/nr w serii: 349 wydano: 1996

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CONTENTS
Introduction........................................................................................................5
0. Announcement of results...............................................................................7
1. Condition (UT).............................................................................................18
2. Weak convergence of solutions...................................................................26
3. Convergence in probability..........................................................................35
4. Stability of SDE's with past-dependent and non-Lipschitz coefficients.........43
5. Stability of Stratonovich SDE's.....................................................................49
6. Skorokhod problem, deterministic case........................................................59
7. Skorokhod problem, nondeterministic case..................................................67
8. SDE's with reflecting boundary.....................................................................74
9. Flows of SDE's with reflecting boundary.......................................................83
10. Numerical schemes for SDE's with reflecting boundary..............................87
Appendix A. Convergence in the Skorokhod topology J₁...............................103
Appendix B. (UT) and convergence of stochastic integrals............................106
Appendix C. Gronwall's lemma.......................................................................106
References....................................................................................................108
Index of symbols.............................................................................................112
Index of terms.................................................................................................113

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Instytut Matematyczny Polskiej Akademii Nauk

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Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 349

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113

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Opis fizyczny

Dissertationes Mathematicae, Tom CCCXLIX

Daty

wydano

1996

otrzymano

1994-10-14

poprawiono

1995-06-09

Twórcy

autor

Słomiński Leszek

Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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1991 Mathematics Subject Classification: Primary 60H20, Secondary 60H99, 60F15.

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Książka - szczegóły

Stability of stochastic differential equations driven by general semimartingales

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