Initial data stability and admissibility of spaces for Itô linear difference equations

Ramazan Kadiev; Pyotr Simonov

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 2, page 185-196
  • ISSN: 0862-7959

Abstract

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The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the p -stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive and expedient than other traditional approaches. For certain equations sufficient conditions of solution stability are given in terms of parameters of those equations.

How to cite

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Kadiev, Ramazan, and Simonov, Pyotr. "Initial data stability and admissibility of spaces for Itô linear difference equations." Mathematica Bohemica 142.2 (2017): 185-196. <http://eudml.org/doc/288112>.

@article{Kadiev2017,
abstract = {The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the $p$-stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive and expedient than other traditional approaches. For certain equations sufficient conditions of solution stability are given in terms of parameters of those equations.},
author = {Kadiev, Ramazan, Simonov, Pyotr},
journal = {Mathematica Bohemica},
keywords = {Itô functional difference equation; stability of solutions; admissibility of spaces},
language = {eng},
number = {2},
pages = {185-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Initial data stability and admissibility of spaces for Itô linear difference equations},
url = {http://eudml.org/doc/288112},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Kadiev, Ramazan
AU - Simonov, Pyotr
TI - Initial data stability and admissibility of spaces for Itô linear difference equations
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 2
SP - 185
EP - 196
AB - The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the $p$-stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive and expedient than other traditional approaches. For certain equations sufficient conditions of solution stability are given in terms of parameters of those equations.
LA - eng
KW - Itô functional difference equation; stability of solutions; admissibility of spaces
UR - http://eudml.org/doc/288112
ER -

References

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  1. Andrianov, D. L., Boundary value problems and control problems for linear difference systems with aftereffect, Russ. Math. 37 (1993), 1-12; translation from Izv. Vyssh. Uchebn. Zaved. Mat. (1993), 3-16. (1993) Zbl0836.34087MR1265616
  2. Azbelev, N. V., Simonov, P. M., Stability of Differential Equations with Aftereffect, Stability and Control: Theory, Methods and Applications 20. Taylor and Francis, London (2003). (2003) Zbl1049.34090MR1965019
  3. Elaydi, S., 10.1006/jmaa.1994.1037, J. Math. Anal. Appl. 181 (1994), 483-492. (1994) Zbl0796.39004MR1260872DOI10.1006/jmaa.1994.1037
  4. Elaydi, S., Zhang, S., Stability and periodicity of difference equations with finite delay, Funkc. Ekvacioj, Ser. Int. 37 (1994), 401-413. (1994) Zbl0819.39006MR1311552
  5. Ikeda, N., Watanabe, S., Stochastic Differential Equations and Diffusion Processes, North-Holland Mathematical Library 24. North-Holland Publishing, Amsterdam; Kodansha Ltd., Tokyo (1981). (1981) Zbl0495.60005MR0637061
  6. Kadiev, R., Sufficient stability conditions for stochastic systems with aftereffect, Differ. Equations 30 (1994), 509-517; translation from Differ. Uravn. (1994), 555-564. (1994) Zbl0824.93069MR1299841
  7. Kadiev, R., Stability of solutions of stochastic functional differential equations, Doctoral dissertation, DSc Habilitation thesis, Makhachkala (2000) (in Russian). 
  8. Kadiev, R., Ponosov, A. V., Stability of linear stochastic functional-differential equations under constantly acting perturbations, Differ. Equations 28 (1992), 173-179; translation from Differ. Uravn. (1992), 198-207. (1992) Zbl0788.60071MR1184920
  9. Kadiev, R., Ponosov, A. V., Relations between stability and admissibility for stochastic linear functional differential equations, Func. Diff. Equ. 12 (2005), 209-244. (2005) Zbl1093.34046MR2137849
  10. Kadiev, R., Ponosov, A. V., 10.1016/j.jmaa.2012.01.003, J. Math. Anal. Appl. 389 (2012), 1239-1250. (2012) Zbl1248.93168MR2879292DOI10.1016/j.jmaa.2012.01.003

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