References
- Annunziato , M. 2002 . Non‐Gaussian equilibrium distribution arising from the Langevin equation . Phys. Rev. E, , 65 ( 21113–1–6 )
- Annunziato , M. 2007 . A finite difference method for piecewise deterministic processes with memory . Math. Model. and Anal., , 12 (2) : 157 – 178 . (doi:10.3846/1392–6292.2007.12.157–178)
- Annunziato , M. 2008 . Analysis of upwind method for piecewise deterministic Markov processes . Comp. Meth. Appl. Math., , 8 : 3 – 20 .
- Annunziato , M. , Grigolini , P. and Riccardi , J. 2000 . Fluctuation‐dissipation process without a time scale . Phys. Rev. E, , 61 : 4801 – 4808 .
- Buckwar , E. and Winkler , R. 2006 . Multistep methods for SDES and their application to problems with small noise . SIAM J. Numer. Anal., , 44 : 779 – 803 .
- Cáceres , O.M. 2003 . Computing a non‐Maxwellian velocity distribution from first principles . Phys. Rev. E, , 67 : 016102 – 016104 .
- Castro , M. , Macías , J. and Parés , C. 2001 . A Q‐scheme for a class of systems of coupled conservation laws with source term. application to a two‐layer 1‐D shallow water system . Math. Mod. Num. Anal., , 35 : 107 – 127 .
- Čiegis , R. , Iliev , O. and Lakdawala , Z. 2007 . On parallel numerical algorithms for simulating industrial filtration problems . Computational Methods in Applied Mathematics, , 7 (2) : 118 – 134 .
- Cockburn , B. , Johnson , C. , Shu , C.‐W. and Tadmor , E. 1998 . Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , volume 1697 , Springer . Lecture Notes in Mathematics
- Costa , O. L.V. and Dufour , F. 2003 . On the Poisson equation for piecewise‐deterministic Markov processes . SIAM J.Control Optim., , 42 : 985 – 1001 .
- Davis , M.H.A. 1993 . Markov Models and Optimizations. , London : Chapman & Hall/CRC .
- Filliger , R. and Hongler , M.O. 2004 . Supersymmetry in random two‐velocity processes . Physica A, , 332 : 141 – 150 .
- Garabedian , P.R. 1964 . Partial Differential Equations , New York : John Wiley & Sons .
- Gardiner , C.W. 1985 . Handbook of Stochastic Methods , 2nd Ed. , Berlin Heidelberg New York : Springer‐Verlag .
- Grama , A. , Gupta , A. , Karypis , G. and Kumar , V. 2003 . Introduction to Parallel Computing , Addison‐Wesley .
- Hillen , T. and Othmer , H.G. 2000 . The diffusion limit of transport equations derived from velocity‐jump processes . SIAM J. Appl. Math., , 61 : 751 – 775 .
- Horsthemke , W. 1999 . Spatial instabilities in reaction random walks with direction‐independent kinetics . Phys. Rev. E, , 60 : 2651 – 2663 .
- Hundsdorfer , W. and Verwer , J.G. 2003 . Numerical solution of Time‐Dependent Adverction‐Diffusion‐Reaction Equations , volume 33 , Springer Verlag, Springer Series in Computational Mathematics .
- Jakeman , E. and Renshaw , E. 1987 . Correlated random‐walk model for scattering. J . Opt. Soc. Am. A, , 4 : 1206 – 1212 .
- Jakeman , E. and Ridley , K.D. 1999 . The statistics of a filtered telegraph signal. J . Phys. A, , 32 : 8803 – 8821 .
- Janssen , J. and Limnios , N. 1999 . Semi‐Markov Models and Applications , Kluwer Academic Publisher .
- Kloeden , P.E. and Platen , E. 1992 . Numerical solution of stochastic differential equation , Berlin Heidelberg New York : Springer‐Verlag .
- LeVeque , Randall J. 1992 . Numerical Methods for conservation Laws , Birkhäuser .
- Mankin , R. , Ainsaar , A. , Haljas , A. and Reiter , E. 2002 . Trichotomous‐noise‐induced catastrophic shifts in symbiotic ecosystems . Phys. Rev. E , 65 ( 051108–1–9 )
- Masoliver , J. and Porrà , J.M. 1993 . Harmonic oscillators driven by colored noise: Crossovers, resonances, and spectra . Phys. Rev. E, , 48 : 4309 – 4319 .
- Milstein , G.N. and Repin , Yu.M. 1972 . Action of Markov process on a system of differential equations . Differential Equations, , 5 : 1010 – 1019 .
- 1969 . Translated from: Differentsial Uravneniya , 5 : 1371 – 1384 .
- Morton , K.W. and Mayers , D.F. 1994 . Numerical Solution of Partial Differential Equations , Cambridge University Press .
- Muñoz‐Ruiz , M.L. and Parés , C. 2007 . Godunov method for nonconservative hyperbolic systems . M2AN, , 41 : 169 – 185 .
- http://mathworld.wolf ram.com/HazardFunction.html (http://mathworld.wolf ram.com/HazardFunction.html)
- Message passing interface. Available Internet: http://www.mcs.anl.gov/mpi (http://www.mcs.anl.gov/mpi)
- Pawula , R.F. 1987 . Approximating distributions from moments . Phys. Rev. A, , 36 : 4996 – 5007 .
- Pawula , R.F. and Rice , O. 1986 . On filtered binary processes . IEEE Trans. Inf. Th. , : IT – 32 . 63 – 72 .
- Starikovičius , V. , Čiegis , R. , Iliev , O. and Lakdawala , Z. 2009 . “ A parallel solver for the 3d simulation of flows through oil filters ” . In Parallel Linear Algebra and Optimization: Advances and Applications , Edited by: Ciegis , R. , Henty , D. , Kagstrōm , B. and Žilinskas , J. volume 27 , 181 – 192 . New‐York : Springer Optimization and Its Applications . ISBN: 978–0–387–09706–0,, Springer
- Starikovičius , V. , Čiegis , R. and Jakušev , A. 2006 . Analysis of upwind and high‐resolution schemes for solving convection dominated problems in porous media . Math. Model. and Anal., , 11 : 451 – 474 .
- Kitahara , K. 1980 . Phase diagrams of noise induced transitions . Prog. Theor. Phys., , 64 : 1233 – 1247 .
- Wolff , R.W. 1989 . Stochastic Modelling and the Theory of Queues. , englewood Cliffs, New Jersey : Prentice Hall .