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Volumn 141, Issue 6, 2010, Pages 1071-1092

On Distributions of Functionals of Anomalous Diffusion Paths

Author keywords

Anomalous diffusion; Continuous time random walk; Feynman Kac equation; Fractional calculus; Levy flights

Indexed keywords


EID: 78649801122     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-010-0086-6     Document Type: Article
Times cited : (90)

References (63)
  • 1
    • 31744442331 scopus 로고    scopus 로고
    • Brownian functionals in physics and computer science
    • Majumdar, S. N.: Brownian functionals in physics and computer science. Curr. Sci. 89, 2076 (2005).
    • (2005) Curr. Sci. , vol.89 , pp. 2076
    • Majumdar, S.N.1
  • 2
    • 24344444415 scopus 로고    scopus 로고
    • Functionals of Brownian motion, localization and metric graphs
    • R341
    • Comtet, A., Desbois, J., Texier, C.: Functionals of Brownian motion, localization and metric graphs. J. Phys. A: Math. Gen. 38, R341 (2005).
    • (2005) J. Phys. A: Math. Gen. , vol.38
    • Comtet, A.1    Desbois, J.2    Texier, C.3
  • 4
    • 0035957434 scopus 로고    scopus 로고
    • Free energy reconstruction from nonequilibrium single-molecule pulling experiments
    • Hummer, G., Szabo, A.: Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc. Natl. Acad. Sci. USA 98, 3658 (2001).
    • (2001) Proc. Natl. Acad. Sci. USA , vol.98 , pp. 3658
    • Hummer, G.1    Szabo, A.2
  • 5
    • 30944438442 scopus 로고    scopus 로고
    • Investigation of a generalized Obukhov model for turbulence
    • Baule, A., Friedrich, R.: Investigation of a generalized Obukhov model for turbulence. Phys. Lett. A 350, 167 (2006).
    • (2006) Phys. Lett. A , vol.350 , pp. 167
    • Baule, A.1    Friedrich, R.2
  • 6
    • 37649032832 scopus 로고    scopus 로고
    • Large-deviation functions for nonlinear functionals of a Gaussian stationary Markov process
    • 051112
    • Majumdar, S. N., Bray, A. J.: Large-deviation functions for nonlinear functionals of a Gaussian stationary Markov process. Phys. Rev. E 65, 051112 (2002).
    • (2002) Phys. Rev. E , vol.65
    • Majumdar, S.N.1    Bray, A.J.2
  • 7
    • 0032397394 scopus 로고    scopus 로고
    • Exponential functionals of Brownian motion and disordered systems
    • Comtet, A., Monthus, C., Yor, M.: Exponential functionals of Brownian motion and disordered systems. J. Appl. Probab. 35, 255 (1998).
    • (1998) J. Appl. Probab. , vol.35 , pp. 255
    • Comtet, A.1    Monthus, C.2    Yor, M.3
  • 9
    • 18444368761 scopus 로고
    • On distributions of certain Wiener functionals
    • Kac, M.: On distributions of certain Wiener functionals. Trans. Am. Math. Soc. 65, 1 (1949).
    • (1949) Trans. Am. Math. Soc. , vol.65 , pp. 1
    • Kac, M.1
  • 10
    • 0023452103 scopus 로고
    • Diffusion in disordered media
    • Havlin, S., ben-Avraham, D.: Diffusion in disordered media. Adv. Phys. 36, 695 (1987).
    • (1987) Adv. Phys. , vol.36 , pp. 695
    • Havlin, S.1    Ben-Avraham, D.2
  • 11
    • 0040307478 scopus 로고
    • Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
    • Bouchaud, J. P., Georges, A.: Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications. Phys. Rep. 195, 127 (1990).
    • (1990) Phys. Rep. , vol.195 , pp. 127
    • Bouchaud, J.P.1    Georges, A.2
  • 12
    • 0002641421 scopus 로고    scopus 로고
    • The random walks's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler, R., Klafter, J.: The random walks's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339, 1 (2000).
    • (2000) Phys. Rep. , vol.339 , pp. 1
    • Metzler, R.1    Klafter, J.2
  • 13
    • 84889299911 scopus 로고    scopus 로고
    • R. Klages, G. Radons, and I. M. Sokolov (Eds.), Weinheim: Wiley
    • Klages, R., Radons, G., Sokolov, I. M. (eds.): Anomalous Transport: Foundations and Applications. Wiley, Weinheim (2008).
    • (2008) Anomalous Transport: Foundations and Applications
  • 14
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • Mandelbrot, B. B., van Ness, J. W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422 (1968).
    • (1968) SIAM Rev. , vol.10 , pp. 422
    • Mandelbrot, B.B.1    van Ness, J.W.2
  • 15
    • 0037026113 scopus 로고    scopus 로고
    • Local and occupation time of a particle diffusing in a random medium
    • 060601
    • Majumdar, S. N., Comtet, A.: Local and occupation time of a particle diffusing in a random medium. Phys. Rev. Lett. 89, 060601 (2002).
    • (2002) Phys. Rev. Lett. , vol.89
    • Majumdar, S.N.1    Comtet, A.2
  • 16
    • 33747688381 scopus 로고    scopus 로고
    • Residence time statistics for normal and fractional diffusion in a force field
    • Barkai, E.: Residence time statistics for normal and fractional diffusion in a force field. J. Stat. Phys. 123, 883 (2006).
    • (2006) J. Stat. Phys. , vol.123 , pp. 883
    • Barkai, E.1
  • 17
    • 0034195174 scopus 로고    scopus 로고
    • Descriptive parameter for photon trajectories in a turbid medium
    • Gandjbakhche, A. H., Weiss, G. H.: Descriptive parameter for photon trajectories in a turbid medium. Phys. Rev. E 61, 6958 (2000).
    • (2000) Phys. Rev. E , vol.61 , pp. 6958
    • Gandjbakhche, A.H.1    Weiss, G.H.2
  • 18
    • 18144419799 scopus 로고    scopus 로고
    • On mean residence and first passage times in finite one-dimensional systems
    • Bar-Haim, A., Klafter, J.: On mean residence and first passage times in finite one-dimensional systems. J. Chem. Phys. 109, 5187 (1998).
    • (1998) J. Chem. Phys. , vol.109 , pp. 5187
    • Bar-Haim, A.1    Klafter, J.2
  • 19
    • 0001211151 scopus 로고
    • Residence times in diffusion processes
    • Agmon, N.: Residence times in diffusion processes. J. Chem. Phys. 81, 3644 (1984).
    • (1984) J. Chem. Phys. , vol.81 , pp. 3644
    • Agmon, N.1
  • 20
    • 77956460747 scopus 로고    scopus 로고
    • The residence time equation
    • Agmon, N.: The residence time equation. Chem. Phys. Lett. 497, 184 (2010).
    • (2010) Chem. Phys. Lett. , vol.497 , pp. 184
    • Agmon, N.1
  • 21
    • 35649003831 scopus 로고    scopus 로고
    • Residence times and other functionals of reflected Brownian motion
    • 041139
    • Grebenkov, D. S.: Residence times and other functionals of reflected Brownian motion. Phys. Rev. E 76, 041139 (2007).
    • (2007) Phys. Rev. E , vol.76
    • Grebenkov, D.S.1
  • 22
    • 84968497856 scopus 로고
    • An occupation time theorem for a class of stochastic processes
    • Lamperti, J.: An occupation time theorem for a class of stochastic processes. Trans. Am. Math. Soc. 88, 380 (1958).
    • (1958) Trans. Am. Math. Soc. , vol.88 , pp. 380
    • Lamperti, J.1
  • 23
    • 33646367402 scopus 로고    scopus 로고
    • Statistical properties of functionals of the paths of a particle diffusing in a one-dimensional random potential
    • 051102
    • Sabhapandit, S., Majumdar, S. N., Comtet, A.: Statistical properties of functionals of the paths of a particle diffusing in a one-dimensional random potential. Phys. Rev. E 73, 051102 (2006).
    • (2006) Phys. Rev. E , vol.73
    • Sabhapandit, S.1    Majumdar, S.N.2    Comtet, A.3
  • 25
    • 34548435692 scopus 로고    scopus 로고
    • NMR survey of reflected Brownian motion
    • Grebenkov, D. S.: NMR survey of reflected Brownian motion. Rev. Mod. Phys. 79, 1077 (2007).
    • (2007) Rev. Mod. Phys. , vol.79 , pp. 1077
    • Grebenkov, D.S.1
  • 27
    • 0141508296 scopus 로고
    • Anomalous transit-time dispersion in amorphous solids
    • Scher, H., Montroll, E.: Anomalous transit-time dispersion in amorphous solids. Phys. Rev. B 12, 2455 (1975).
    • (1975) Phys. Rev. B , vol.12 , pp. 2455
    • Scher, H.1    Montroll, E.2
  • 28
    • 33745041973 scopus 로고    scopus 로고
    • Anomalous diffusion of inertial, weakly damped particles
    • 230601
    • Friedrich, R., Jenko, F., Baule, A., Eule, S.: Anomalous diffusion of inertial, weakly damped particles. Phys. Rev. Lett. 96, 230601 (2006).
    • (2006) Phys. Rev. Lett. , vol.96
    • Friedrich, R.1    Jenko, F.2    Baule, A.3    Eule, S.4
  • 29
    • 70449850116 scopus 로고    scopus 로고
    • Fractional Feynman-Kac equation for non-Brownian functionals
    • 190201
    • Turgeman, L., Carmi, S., Barkai, E.: Fractional Feynman-Kac equation for non-Brownian functionals. Phys. Rev. Lett. 103, 190201 (2009).
    • (2009) Phys. Rev. Lett. , vol.103
    • Turgeman, L.1    Carmi, S.2    Barkai, E.3
  • 30
    • 0000078998 scopus 로고    scopus 로고
    • From continuous time random walks to the fractional Fokker-Planck equation
    • Barkai, E., Metzler, R., Klafter, J.: From continuous time random walks to the fractional Fokker-Planck equation. Phys. Rev. E 61, 132 (2000).
    • (2000) Phys. Rev. E , vol.61 , pp. 132
    • Barkai, E.1    Metzler, R.2    Klafter, J.3
  • 31
    • 4043102385 scopus 로고    scopus 로고
    • Limit theorems for continuous-time random walks with infinite mean waiting times
    • Meerschaert, M. M., Scheffler, H. P.: Limit theorems for continuous-time random walks with infinite mean waiting times. J. Appl. Probab. 41, 623 (2004).
    • (2004) J. Appl. Probab. , vol.41 , pp. 623
    • Meerschaert, M.M.1    Scheffler, H.P.2
  • 32
    • 21844503941 scopus 로고
    • Asymptotic distributions of continuous-time random walks: A probabilistic approach
    • Kotulski, M.: Asymptotic distributions of continuous-time random walks: A probabilistic approach. J. Stat. Phys. 81, 777 (1995).
    • (1995) J. Stat. Phys. , vol.81 , pp. 777
    • Kotulski, M.1
  • 33
    • 0000700033 scopus 로고
    • Transport properties of the continuous-time random walk with a long-tailed waiting-time density
    • Weissman, H., Weiss, G. H., Havlin, S.: Transport properties of the continuous-time random walk with a long-tailed waiting-time density. J. Stat. Phys. 57, 301 (1989).
    • (1989) J. Stat. Phys. , vol.57 , pp. 301
    • Weissman, H.1    Weiss, G.H.2    Havlin, S.3
  • 34
    • 0001553919 scopus 로고
    • Fractional diffusion and wave equations
    • Schneider, W. R., Wyss, W.: Fractional diffusion and wave equations. J. Math. Phys. 30, 134 (1988).
    • (1988) J. Math. Phys. , vol.30 , pp. 134
    • Schneider, W.R.1    Wyss, W.2
  • 35
    • 4244190920 scopus 로고
    • Langevin equations for continuous time Lévy flights
    • Fogedby, H. C.: Langevin equations for continuous time Lévy flights. Phys. Rev. E 50, 1657 (1994).
    • (1994) Phys. Rev. E , vol.50 , pp. 1657
    • Fogedby, H.C.1
  • 36
    • 33846621507 scopus 로고    scopus 로고
    • Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation
    • 016708
    • Magdziarz, M., Weron, A., Weron, K.: Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation. Phys. Rev. E 75, 016708 (2007).
    • (2007) Phys. Rev. E , vol.75
    • Magdziarz, M.1    Weron, A.2    Weron, K.3
  • 37
    • 36749036093 scopus 로고    scopus 로고
    • Continuous-time random walks: Simulation of continuous trajectories
    • 061102
    • Kleinhans, D., Friedrich, R.: Continuous-time random walks: Simulation of continuous trajectories. Phys. Rev. E 76, 061102 (2007).
    • (2007) Phys. Rev. E , vol.76
    • Kleinhans, D.1    Friedrich, R.2
  • 38
    • 0035537470 scopus 로고    scopus 로고
    • Statistics of the occupation time of renewal processes
    • Godrèche, C., Luck, J. M.: Statistics of the occupation time of renewal processes. J. Stat. Phys. 104, 489 (2001).
    • (2001) J. Stat. Phys. , vol.104 , pp. 489
    • Godrèche, C.1    Luck, J.M.2
  • 40
    • 18144424024 scopus 로고    scopus 로고
    • Non-ergodicity of blinking nano crystals and other Lévy walk processes
    • 080601
    • Margolin, G., Barkai, E.: Non-ergodicity of blinking nano crystals and other Lévy walk processes. Phys. Rev. Lett. 94, 080601 (2005).
    • (2005) Phys. Rev. Lett. , vol.94
    • Margolin, G.1    Barkai, E.2
  • 41
    • 33644506786 scopus 로고    scopus 로고
    • Non-ergodicity of a time series obeying Lévy statistics
    • Margolin, G., Barkai, E.: Non-ergodicity of a time series obeying Lévy statistics. J. Stat. Phys. 122, 137 (2006).
    • (2006) J. Stat. Phys. , vol.122 , pp. 137
    • Margolin, G.1    Barkai, E.2
  • 42
    • 59749105954 scopus 로고    scopus 로고
    • Beyond quantum jumps: Blinking nano-scale light emitters
    • Stefani, F. D., Hoogenboom, J. P., Barkai, E.: Beyond quantum jumps: Blinking nano-scale light emitters. Phys. Today 62, 34 (2009).
    • (2009) Phys. Today , vol.62 , pp. 34
    • Stefani, F.D.1    Hoogenboom, J.P.2    Barkai, E.3
  • 43
    • 0000893434 scopus 로고
    • Generalized arc-sine laws for one-dimensional diffusion processes and random walks
    • Watanabe, S.: Generalized arc-sine laws for one-dimensional diffusion processes and random walks. Proc. Symp. Pure Math. 57, 157 (1995).
    • (1995) Proc. Symp. Pure Math. , vol.57 , pp. 157
    • Watanabe, S.1
  • 44
    • 0003021436 scopus 로고
    • On some connections between probability theory and differential and integral equations
    • Berkeley, CA, USAUniversity of California Press
    • Kac, M.: On some connections between probability theory and differential and integral equations. In: Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA, p.189 (1951). University of California Press.
    • (1951) Second Berkeley Symposium on Mathematical Statistics and Probability , pp. 189
    • Kac, M.1
  • 45
    • 34547327313 scopus 로고    scopus 로고
    • Competition between subdiffusion and Lévy flights: a Monte Carlo approach
    • 056702
    • Magdziarz, M., Weron, A.: Competition between subdiffusion and Lévy flights: a Monte Carlo approach. Phys. Rev. E 75, 056702 (2007).
    • (2007) Phys. Rev. E , vol.75
    • Magdziarz, M.1    Weron, A.2
  • 46
    • 73649101890 scopus 로고    scopus 로고
    • Anomalous diffusion and generalized Sparre Andersen scaling
    • Dybiec, B., Gudowska-Nowak, E.: Anomalous diffusion and generalized Sparre Andersen scaling. EPL 88, 10003 (2009).
    • (2009) Epl , vol.88 , pp. 10003
    • Dybiec, B.1    Gudowska-Nowak, E.2
  • 48
    • 0035305938 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equation, solution, and application
    • 046118
    • Barkai, E.: Fractional Fokker-Planck equation, solution, and application. Phys. Rev. E 63, 046118 (2001).
    • (2001) Phys. Rev. E , vol.63
    • Barkai, E.1
  • 49
    • 33947576544 scopus 로고    scopus 로고
    • Precise asymptotics for a random walkers maximum
    • Comtet, A., Majumdar, S. N.: Precise asymptotics for a random walkers maximum. J. Stat. Mech. P06013 (2005).
    • (2005) J. Stat. Mech.
    • Comtet, A.1    Majumdar, S.N.2
  • 51
    • 75849116801 scopus 로고    scopus 로고
    • Extreme value statistics from the real space renormalization group: Brownian motion, Bessel processes and continuous time random walks
    • Schehr, G., Le-Doussal, P.: Extreme value statistics from the real space renormalization group: Brownian motion, Bessel processes and continuous time random walks. J. Stat. Mech. P01009 (2010).
    • (2010) J. Stat. Mech.
    • Schehr, G.1    Le-Doussal, P.2
  • 53
    • 74549195113 scopus 로고    scopus 로고
    • Hitting probability for anomalous diffusion processes
    • 020602
    • Majumdar, S. N., Rosso, A., Zoia, A.: Hitting probability for anomalous diffusion processes. Phys. Rev. Lett. 104, 020602 (2010).
    • (2010) Phys. Rev. Lett. , vol.104
    • Majumdar, S.N.1    Rosso, A.2    Zoia, A.3
  • 54
    • 18144408075 scopus 로고    scopus 로고
    • Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach
    • Metzler, R., Barkai, E., Klafter, J.: Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach. Phys. Rev. Lett. 82, 3563 (1999).
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 3563
    • Metzler, R.1    Barkai, E.2    Klafter, J.3
  • 55
    • 0034315319 scopus 로고    scopus 로고
    • Schrödinger equations with fractional Laplacians
    • Hu, Y., Kallianpur, G.: Schrödinger equations with fractional Laplacians. Appl. Math. Optim. 42, 281 (2000).
    • (2000) Appl. Math. Optim. , vol.42 , pp. 281
    • Hu, Y.1    Kallianpur, G.2
  • 56
    • 0034271488 scopus 로고    scopus 로고
    • Fractional quantum mechanics
    • Laskin, N.: Fractional quantum mechanics. Phys. Rev. E 62, 3135 (2000).
    • (2000) Phys. Rev. E , vol.62 , pp. 3135
    • Laskin, N.1
  • 57
    • 41349084761 scopus 로고    scopus 로고
    • Fractional Schrödinger equation
    • 056108
    • Laskin, N.: Fractional Schrödinger equation. Phys. Rev. E 66, 056108 (2002).
    • (2002) Phys. Rev. E , vol.66
    • Laskin, N.1
  • 58
    • 4544250038 scopus 로고    scopus 로고
    • Time fractional Schrödinger equation
    • Naber, M.: Time fractional Schrödinger equation. J. Math. Phys. 45, 3339 (2004).
    • (2004) J. Math. Phys. , vol.45 , pp. 3339
    • Naber, M.1
  • 59
    • 34247620479 scopus 로고    scopus 로고
    • Generalized fractional Schrödinger equation with spacetime fractional derivatives
    • 043502
    • Wang, S., Xu, M.: Generalized fractional Schrödinger equation with spacetime fractional derivatives. J. Math. Phys. 48, 043502 (2007).
    • (2007) J. Math. Phys. , vol.48
    • Wang, S.1    Xu, M.2
  • 60
    • 70349479770 scopus 로고    scopus 로고
    • Fractional-time quantum dynamics
    • 022103
    • Iomin, A.: Fractional-time quantum dynamics. Phys. Rev. E 80, 022103 (2009).
    • (2009) Phys. Rev. E , vol.80
    • Iomin, A.1
  • 61
    • 36249011538 scopus 로고    scopus 로고
    • Distribution of time-averaged observables for weak ergodicity breaking
    • 210601
    • Rebenshtok, A., Barkai, E.: Distribution of time-averaged observables for weak ergodicity breaking. Phys. Rev. Lett. 99, 210601 (2007).
    • (2007) Phys. Rev. Lett. , vol.99
    • Rebenshtok, A.1    Barkai, E.2
  • 62
    • 27744586782 scopus 로고    scopus 로고
    • Weak ergodicity breaking in the continuous-time random walk
    • 240602
    • Bel, G., Barkai, E.: Weak ergodicity breaking in the continuous-time random walk. Phys. Rev. Lett. 94, 240602 (2005).
    • (2005) Phys. Rev. Lett. , vol.94
    • Bel, G.1    Barkai, E.2
  • 63
    • 54949159002 scopus 로고    scopus 로고
    • Weakly non-ergodic statistical physics
    • Rebenshtok, A., Barkai, E.: Weakly non-ergodic statistical physics. J. Stat. Phys. 133, 565 (2008).
    • (2008) J. Stat. Phys. , vol.133 , pp. 565
    • Rebenshtok, A.1    Barkai, E.2


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