Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures

B. Maslowski; I. Simão

Colloquium Mathematicae (1997)

  • Volume: 72, Issue: 1, page 147-171
  • ISSN: 0010-1354

How to cite

top

Maslowski, B., and Simão, I.. "Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures." Colloquium Mathematicae 72.1 (1997): 147-171. <http://eudml.org/doc/210450>.

@article{Maslowski1997,
author = {Maslowski, B., Simão, I.},
journal = {Colloquium Mathematicae},
keywords = {invariant measures; mixing; stochastic semilinear equations; ergodicity},
language = {eng},
number = {1},
pages = {147-171},
title = {Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures},
url = {http://eudml.org/doc/210450},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Maslowski, B.
AU - Simão, I.
TI - Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 1
SP - 147
EP - 171
LA - eng
KW - invariant measures; mixing; stochastic semilinear equations; ergodicity
UR - http://eudml.org/doc/210450
ER -

References

top
  1. [1] L. Arnold, R. F. Curtain and P. Kotelenez, Nonlinear stochastic evolution equations in Hilbert space, Report no. 17, Forschungsschwerpunkt Dynamische Systeme, Universität Bremen 1980. 
  2. [2] A. Chojnowska-Michalik and B. Gołdys, Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces, Probab. Theory Related Fields 102 (1995), 331-356. 
  3. [3] G. Da Prato and A. Debussche, Stochastic Cahn-Hilliard equation, preprint Scuola Normale Superiore Pisa no. 5/1994. 
  4. [4] G. Da Prato, D. Elworthy and J. Zabczyk, Strong Feller property for stochastic semilinear equations, Stochastic Anal. Appl. 13 (1993), 35-45. Zbl0817.60081
  5. [5] G. Da Prato and D. Gątarek, Stochastic Burgers equation with correlated noise, Stochastics Stochastics Rep. 52 (1995), 29-41. Zbl0853.35138
  6. [6] G. Da Prato, D. Gątarek and J. Zabczyk, Invariant measures for semilinear stochastic equations, Stochastic Anal. Appl. 10 (1992), 387-408. Zbl0758.60057
  7. [7] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992. Zbl0761.60052
  8. [8] G. Da Prato and J. Zabczyk, Non-explosion, boundedness and ergodicity for stochastic semilinear equations, J. Differential Equations 98 (1992), 181-195. Zbl0762.60052
  9. [9] F. Flandoli and B. Maslowski, Ergodicity of the 2-D Navier-Stokes equation under random perturbations, Comm. Math. Phys. 171 (1995), 119-141. Zbl0845.35080
  10. [10] A. Friedman, Stochastic Differential Equations and Applications, Vol. I, Academic Press, New York, 1975. Zbl0323.60056
  11. [11] M. Fuhrman, Densities of Gaussian measures and regularity of non-symmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, IMPAN, Warszawa, Preprint 528 (1994). 
  12. [12] D. Fujiwara, Concrete characterization of the domain of fractional powers of some elliptic differential operators of the second order, Proc. Japan Acad. Ser. A Math. Sci. 43 (1967), 82-86. Zbl0154.16201
  13. [13] D. Gątarek and B. Gołdys, On solving stochastic equation by the change of drift with application to optimal control, in: Stochastic PDE's and Applications, Proceedings, Pitman, 1992, 180-190. Zbl0797.60047
  14. [14] D. Gątarek and B. Gołdys, On invariant measures for diffusions on Banach spaces, Potential Anal., to appear. Zbl0894.60057
  15. [15] B. Gołdys, On some regularity properties of solutions to stochastic evolution equations in Hilbert spaces, Colloq. Math. 58 (1990), 327-338. Zbl0704.60059
  16. [16] S. Jacquot and G. Royer, Ergodicity of stochastic plates, Probab. Theory Related Fields, submitted. Zbl0822.60053
  17. [17] S. Jacquot and G. Royer, Ergodicité d'une classe d'équations aux dérivées partielles stochastiques, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 231-236. 
  18. [18] G. Kallianpur, Zero-one laws for Gaussian processes, Trans. Amer. Math. Soc. 149 (1970), 199-211. Zbl0234.60032
  19. [19] R. Z. Khas'minskiĭ, Ergodic properties of recurrent diffusion processes and stabilization of the solutions to the Cauchy problem for parabolic equations, Theory Probab. Appl. 5 (1960), 179-196. 
  20. [20] P. Kotelenez, A maximal inequality for stochastic convolution integrals on Hilbert spaces and space-time regularity of linear stochastic partial differential equations, Stochastics 21 (1987), 345-358. Zbl0622.60065
  21. [21] A. Lasota, Statistical stability of deterministic systems, in: Proceedings Würzburg 1982, Lecture Notes in Math. 1017, Springer, Berlin, 1983, 386-419. Zbl0532.47027
  22. [22] A. Lasota and M. C. Mackey, Chaos, fractals, and noise, Springer, New York, 1994. Zbl0784.58005
  23. [23] A. Lasota and J. A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384. Zbl0524.28021
  24. [24] G. Leha and G. Ritter, Lyapunov-type conditions for stationary distributions of diffusion processes on Hilbert spaces, Stochastics Stochastics Rep. 48 (1994), 195-225. Zbl0828.60063
  25. [25] R. Manthey and B. Maslowski, Qualitative behaviour of solutions of stochastic reaction-diffusion equations, Stochastic Process. Appl. 43 (1992), 265-289. Zbl0761.60055
  26. [26] B. Maslowski, On probability distributions of solutions of semilinear stochastic evolution equations, Stochastics Stochastics Rep. 45 (1993), 17-44. Zbl0792.60058
  27. [27] B. Maslowski, An application of l-condition in the theory of stochastic differential equations, Časopis Pěst. Mat. 112 (1987), 296-307. Zbl0645.60063
  28. [28] B. Maslowski, Strong Feller property for semilinear stochastic evolution equations and applications, in: Proc. Jabłonna 1988, Lecture Notes in Control and Inform. Sci. 136, Springer, Berlin, 1989, 210-225. 
  29. [29] B. Maslowski and J. Seidler, Ergodic properties of recurrent solutions of stochastic evolution equations, Osaka J. Math. 31 (1994), 965-1003. Zbl0820.60040
  30. [30] S. Peszat and J. Zabczyk, Strong Feller property and irreducibility for diffusions on Hilbert spaces, Ann. Probab. 23 (1995), 157-172. Zbl0831.60083
  31. [31] J. Seidler, Da Prato-Zabczyk's maximal inequality revisited I, Math. Bohem. 118 (1993), 67-106. Zbl0785.35115
  32. [32] J. Seidler, Ergodic behaviour of stochastic parabolic equations, Czechoslovak Math. J., to appear. Zbl0935.60041
  33. [33] I. Simão, Regular transition densities for infinite dimensional diffusions, Stochastic Anal. Appl. 11 (1993), 309-336. Zbl0777.60076
  34. [34] I. Simão, A conditioned Ornstein-Uhlenbeck process on a Hilbert space, ibid. 9 (1991), 85-98. Zbl0722.60052
  35. [35] I. Simão, Pinned Ornstein-Uhlenbeck processes on an infinite dimensional space, Preprint CMAF, University of Lisbon, 1995. Zbl0945.60079

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.