Solvability of dichotomous flows, dichotomous diffusion and generalizations

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5114, Issue , 2003, Pages 40-46

  Balakrishnan, V ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Correlated noise; Dichotomous flow; Generalized diffusion; Master equation; Multi level Markov noise

Indexed keywords

BROWNIAN MOVEMENT; DIFFUSION; INTEGRODIFFERENTIAL EQUATIONS; INTERPOLATION; MARKOV PROCESSES; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION;

CORRELATED NOISE; DICHOTOMOUS DIFFUSION; DICHOTOMOUS FLOW; MARKOV NOISE;

SPURIOUS SIGNAL NOISE;

EID: 0041322772     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.497510     Document Type: Conference Paper

References (17)

1. P. Jung, "Colored noise in dynamical systems: Some exact solutions", in Stochastic Dynamics, Editors L. Schimansky-Geier and T. Pöschel, pp. 23-31 (Springer-Verlag, Berlin, 1997).
2. K. Kitahara, W. Horsthemke and R. Lefever, "Coloured-noise-induced transitions: Exact results for external dichotomous Markovian noise", Phys. Lett. A 70, 377-380 (1979).
3. W. Horsthemke and R. Lefever, Noise Induced Transitions (Springer-Verlag, Berlin, 1984), Ch. 9.
4. C. Van den Broeck, "From Stratanovich calculus to noise-induced phase transitions", in Stochastic Dynamics, Editors L. Schimansky-Gaier and T. Pöschel, pp. 7-14 (Springer-Verlag, Berlin, 1997).
5. C. Van den Broeck, "Taylor dispersion revisited", Physica A 168, 677-696 (1990).
6. V. Balakrishnan, C. Van den Broeck and P. Hänggi, "First-passage times of non-Markovian processes: The case of a reflecting boundary", Phys. Rev. A 38, 4213-4222 (1988).
7. J. Olarrea, J.M. Parrondo and F.J. de la Rubia, "Escape statistics for systems driven by dichotomous noise. I. General theory", J. Stat. Phys. 79, 669-682 (1995)
8. J. Olarrea, J.M. Parrondo and F.J. de la Rubia, "Escape statistics for systems driven by dichotomous noise. II. The imperfect pitchfork bifurcation as a case study", J. Stat. Phys. 79, 683-699 (1995).
9. J.M. Sancho, "Stochastic processes driven by dichotomous noise: Some exact results", J. Math. Phys. 25, 354-359 (1984).
10. V. Balakrishnan and C. Van den Broeck, "Solvability of the master equation for dichotomous flow", Phys. Rev. E 65, 012101 (1-4) (2001).
11. V. Balakrishnan, C. Van den Broeck and I. Bena, "Stochastically perturbed flows: delayed and interrupted evolution", Stoch. Dyn. 1, 537-551 (2001).
12. C. Van den Broeck, "On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process", J. Stat. Phys. 31, 467-483 (1983).
13. V.E. Shapiro and V.M. Loginov, "Formulae of differentiation and their use for solving stochastic equations", Physica A 91, 563-574 (1978).
14. V. Balakrishnan and S. Chaturvedi, "Persistent diffusion on a line", Physica A 148, 581-596 (1988).
15. M.O. Höngler, Helv. Phys. Acta 52, 280 (1979).
16. C. Van den Broeck and R.M. Mazo, "The asymptotic dispersion of particles in N-layer systems", J. Chem. Phys. 81, 3624-3634 (1984).
17. K.S. Mallesh and N. Mukunda, "The algebra and geometry of SU (3) matrices", Pramana - J. Phys. 49, 371-383 (1997).