Stability of stochastic differential equations driven by general semimartingales

Słomiński Leszek

  • 1996

Abstract

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

How to cite

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Słomiński Leszek. Stability of stochastic differential equations driven by general semimartingales. 1996. <http://eudml.org/doc/275824>.

@book{SłomińskiLeszek1996,
abstract = { 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 1991 Mathematics Subject Classification: Primary 60H20, Secondary 60H99, 60F15.},
author = {Słomiński Leszek},
keywords = {stochastic differential equations; semimartingales; convergence in law; Stratonovich equation},
language = {eng},
title = {Stability of stochastic differential equations driven by general semimartingales},
url = {http://eudml.org/doc/275824},
year = {1996},
}

TY - BOOK
AU - Słomiński Leszek
TI - Stability of stochastic differential equations driven by general semimartingales
PY - 1996
AB - 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 1991 Mathematics Subject Classification: Primary 60H20, Secondary 60H99, 60F15.
LA - eng
KW - stochastic differential equations; semimartingales; convergence in law; Stratonovich equation
UR - http://eudml.org/doc/275824
ER -

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