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Theory of stochastic systems with singular multiplicative noise


Sumy State University, ul. Rimskogo-Korsakova 2, Sumy, 244007, Ukraine

Noisy, interacting, stochastic systems are analyzed for the case in which their noise intensity varies with the hydrodynamic mode amplitude x according to the power law x2a, x \in [0, 1]. It is shown that the phase space domain of definition of the stochastic variable x forms a self-affine set of fractal dimensionality D = 2(1-a). Using the gauge procedure, a system of calculus is chosen which is not reducible either to the Ito case or the Stratonovich case. By generalizing the microscopic picture of phase transitions it is demonstrated that the system may reduce its symmetry (for 1 < D \leqslant 2) or lose ergodicity (for 0 < D \leqslant 1). Over the entire interval D \in [0, 2], a noise-induced transition is shown to be possible.

Fulltext pdf (523 KB)
Fulltext is also available at DOI: 10.1070/PU1998v041n03ABEH000377
PACS: 05.40.+j, 05.70.Fh, 64.60.−i, 82.20.Fd (all)
DOI: 10.1070/PU1998v041n03ABEH000377
URL: https://ufn.ru/en/articles/1998/3/c/
000073306100003
Citation: Olemskoi A I "Theory of stochastic systems with singular multiplicative noise" Phys. Usp. 41 269–301 (1998)
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Оригинал: Олемской А И «Теория стохастических систем с сингулярным мультипликативным шумом» УФН 168 287–321 (1998); DOI: 10.3367/UFNr.0168.199803c.0287

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  12. Khomenko A V, Lyashenko I A Uspekhi Fizicheskikh Nauk 182 1081 (2012)
  13. Knyaz’ I A Eur. Phys. J. B 83 235 (2011)
  14. Olemskoi A I, Yushchenko O V, Zhilenko T I Phys. Solid State 53 845 (2011)
  15. Koverda V P, Skokov V N Physica A: Statistical Mechanics And Its Applications 388 1804 (2009)
  16. Kolesnichenko A V Sol Syst Res 42 391 (2008)
  17. Koverda V P, Skokov V N Tech. Phys. 52 1391 (2007)
  18. Koverda V P, Skokov V N, Reshetnikov A V J. Engin. Thermophys. 16 130 (2007)
  19. Olemskoi A I, Kharchenko D O Variational and Extremum Principles in Macroscopic Systems (2005) p. 695
  20. Olemskoi A I, Kharchenko D O, Knyaz’ I A Phys. Rev. E 71 (4) (2005)
  21. Kharchenko D O Usp. Fiz. Met. 6 1 (2005)
  22. Koverda V P, Skokov V N et al High Temp 43 634 (2005)
  23. Khomenko A V, Lyashenko I A Tech. Phys. 50 1408 (2005)
  24. Olemskoi A I, Khomenko A V, Olemskoi D A Physica A: Statistical Mechanics And Its Applications 332 185 (2004)
  25. Koverda V P, Skokov V N Tech. Phys. 49 1104 (2004)
  26. Khomenko A V Physics Letters A 329 140 (2004)
  27. Olemskoi A I, Yushchenko O V Tech. Phys. 48 1233 (2003)
  28. Olemskoi A I, Khomenko A V, Kharchenko D O Physica A: Statistical Mechanics And Its Applications 323 263 (2003)
  29. Savenkov G G Tech. Phys. 47 1529 (2002)
  30. Kharchenko D O Physica A: Statistical Mechanics And Its Applications 308 113 (2002)
  31. KOLEVA MARIA K, COVACHEV VALÉRY C Fluct. Noise Lett. 01 R131 (2001)
  32. Olemskoi A I, Brazhnyi V A Phys. Solid State 43 386 (2001)
  33. Olemskoi A I Uspekhi Fizicheskikh Nauk 171 503 (2001)
  34. Olemskoi A I, Kharchenko D O Physica A: Statistical Mechanics And Its Applications 293 178 (2001)
  35. Olemskoi A I, Khomenko A V, Koverda V P Physica A: Statistical Mechanics And Its Applications 284 79 (2000)
  36. Koleva M K, Eiyias A E, Petrov L A Metal-Ligand Interactions in Chemistry, Physics and Biology Chapter 15 (2000) p. 353
  37. Olemskoi A I Jetp Lett. 71 285 (2000)
  38. Olemskoi A I, Kharchenko D O Phys. Solid State 42 532 (2000)
  39. Olemskoi A I, Klepikov V F Physics Reports 338 571 (2000)
  40. Gudyma Yu V Tech. Phys. Lett. 25 164 (1999)
  41. Olemskoi A I Physica A: Statistical Mechanics And Its Applications 270 444 (1999)
  42. Olemskoi A I Jetp Lett. 69 423 (1999)
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