Periodic and almost periodic flows of periodic Ito equations

C. Tudor

Mathematica Bohemica (1992)

  • Volume: 117, Issue: 3, page 225-238
  • ISSN: 0862-7959

Abstract

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Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the l p -bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.

How to cite

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Tudor, C.. "Periodic and almost periodic flows of periodic Ito equations." Mathematica Bohemica 117.3 (1992): 225-238. <http://eudml.org/doc/29438>.

@article{Tudor1992,
abstract = {Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the $l^p$-bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.},
author = {Tudor, C.},
journal = {Mathematica Bohemica},
keywords = {trajectory of an almost periodic flow; uniform asymptotic stability; Itô equations; periodic and almost periodic flows; asymptotically almost periodic solution; trajectory of an almost periodic flow; uniform asymptotic stability; Itô equations},
language = {eng},
number = {3},
pages = {225-238},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic and almost periodic flows of periodic Ito equations},
url = {http://eudml.org/doc/29438},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Tudor, C.
TI - Periodic and almost periodic flows of periodic Ito equations
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 3
SP - 225
EP - 238
AB - Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the $l^p$-bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.
LA - eng
KW - trajectory of an almost periodic flow; uniform asymptotic stability; Itô equations; periodic and almost periodic flows; asymptotically almost periodic solution; trajectory of an almost periodic flow; uniform asymptotic stability; Itô equations
UR - http://eudml.org/doc/29438
ER -

References

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  1. A. Halanay T. Morozan, C. Tudor, Bounded solutions of affine stochastic differential equations and stability, Časopis pro pěstování matematiky 111 (1986), 127-136. (1986) MR0847312
  2. A. Halanay T. Morozan, C. Tudor, 10.1080/17442508708833461, Stochastics 21 (1987), 287-301. (1987) MR0905050DOI10.1080/17442508708833461
  3. A. Haraux, 10.1016/0022-0396(87)90039-8, J. Differential Equations 66 (1987), 51-61. (1987) Zbl0608.34049MR0871570DOI10.1016/0022-0396(87)90039-8
  4. N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland, 1981. (1981) Zbl0495.60005MR1011252
  5. R. Khasminskii, Stability of Differential Equations under Random Perturbations, Nauka, 1969. (In russian.) (1969) 
  6. Y. Miyahara, 10.1017/S0027763000014951, Nagoya Math. J. 47 (1972), 111-144. (1972) Zbl0222.60036MR0319269DOI10.1017/S0027763000014951
  7. T. Morozan, Bounded and periodic solutions of affine stochastic differential equations, Studii si Cercetari Matematice 38 (1986), 523-527. (1986) Zbl0623.60075MR0878757
  8. W. Römisch, A. Wakolbinger, On convergence rates of approximate solutions of stochastic equations, Lect. Notes in Control and Information Sciences 96, Springer-Verlag, 1986. (1986) 
  9. A. Skorokhod, Studies in the Theory of Random Processes, Addison-Wesley, 1965. (1965) Zbl0146.37701MR0185620
  10. D. V. Stroock, S. R. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, 1979. (1979) Zbl0426.60069MR0532498
  11. C. Tudor, 10.1016/0022-0396(88)90002-2, J. Differential Equations 72 no. 2 (1988), 200-217. (1988) Zbl0649.60072MR0952895DOI10.1016/0022-0396(88)90002-2
  12. C. Vârsan, 10.2748/tmj/1178227731, Tôhoku Math. J. 41 no. 4 (1989), 609-618. (1989) MR1025326DOI10.2748/tmj/1178227731

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