Path integral for the probability of the trajectories generated by fractional dynamics subject to Gaussian white noise

Applied Mathematics Letters

Volumn 20, Issue 8, 2007, Pages 846-852

  Jumarie, Guy ^a  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

Author keywords

Fractional noise; Fractional Taylor's series; Path integral; Path probability

Indexed keywords

GAUSSIAN NOISE (ELECTRONIC); PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; WHITE NOISE;

FRACTIONAL NOISE; FRACTIONAL TAYLOR'S SERIES; PATH INTEGRAL; PATH PROBABILITY;

INTEGRAL EQUATIONS;

EID: 34047274579     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2006.08.015     Document Type: Article

References (10)

1. Caputo M. Linear model of dissipation whose Q is almost frequency dependent II. Geophys. J. Roy. Astr. Soc. 13 (1967) 529-539
2. Decreusefond L., and Ustunel A.S. Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177-214
3. Djrbashian M.M., and Nersesian A.B. Fractional derivative and the Cauchy problem for differential equations of fractional order. Izv. Acad. Nauk Armjanskoi SSR 3 1 (1968) 3-29 (in Russian)
4. Haken H. Synergetics (1978), Springer-Verlag
5. Janes E.T. Information theory and statistical mechanics. Phys. Rev. 106 (1957) 620
6. Janes E.T. Information theory and statistical mechanics. Phys. Rev. 108 (1957) 171
7. α. Appl. Math. Lett. 18 (2005) 739-748
8. Jumarie G. On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion. Appl. Math. Lett. 18 (2005) 817-826
9. Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results. Comput. Math. Appl. 51 (2006) 1367-1376
10. G. Jumarie, Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor's series of nondifferentiable functions, Chaos Solitons Fractal (in press)