Abstract
We introduce a new class of stochastic processes in
References
[1] I. Müller and T. Ruggeri, Rational Extended Thermodynamics, Springer, Berlin, 2013.Search in Google Scholar
[2] D. Jou, J. Casas-Vazquez and G. Lebon, Extended Irreversible Thermodynamics, Springer, Berlin, 1996.10.1007/978-3-642-97671-1Search in Google Scholar
[3] D. W. Tang and N. Araki, Wavy, wavelike, diffusive thermal responses of finite rigid slabs to high-speed heating of laser-pulser, Int. J. Heat Mass Transfer 42 (1999), 855–860.10.1016/S0017-9310(98)00244-0Search in Google Scholar
[4] D. D. Joseph and L. Preziosi, Heat waves, Rev. Mod. Phys. 61 (1989), 41–73.10.1103/RevModPhys.61.41Search in Google Scholar
[5] S. R. de Groot and P. Mazur, Non-equilibrium Thermodynamics, Dover, New York, 1984.Search in Google Scholar
[6] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise, Springer-Verlag, New York, 1994.10.1007/978-1-4612-4286-4Search in Google Scholar
[7] H. C. Öttinger, Stochastic Processes in Polymeric Fluids, Springer, Berlin, 1996.10.1007/978-3-642-58290-5Search in Google Scholar
[8] M. Kac, A stochastic model related to the telegrapher’s equation, Rocky Mount. J. Math. 4 (1974), 497–509.10.1216/RMJ-1974-4-3-497Search in Google Scholar
[9] C. Körner and H. W. Bergmann, The physical defects of the hyperbolic heat conduction equation, Appl. Phys. A 67 (1998), 397–401.10.1007/s003390050792Search in Google Scholar
[10] A. Brasiello, S. Crescitelli and M. Giona, One-dimensional hyperbolic transport: positivity and admissible boundary conditions derived from the wave formulation, Phys. A 449 (2016), 176–191.10.1016/j.physa.2015.12.111Search in Google Scholar
[11] G. H. Weiss, Some applications of persistent random walks and the telegrapher’s equation, Phys. A 311 (2002), 381–410.10.1016/S0378-4371(02)00805-1Search in Google Scholar
[12] I. Bena, Dichotomous Markov noise: exact results for out-of-equilibrium systems, Int. J. Mod. Phys. B 20 (2006), 2825–2888.10.1142/S0217979206034881Search in Google Scholar
[13] W. Horsthemke and R. Lefever, Noise-Induced Transitions, Springer, Berlin, 2006.Search in Google Scholar
[14] E. Wong and M. Zakai, On the relation between ordinary and stochastic differential equations, Int. J. Eng. Sci. 3 (1965), 213–229.10.1016/0020-7225(65)90045-5Search in Google Scholar
[15] A. V. Plyukhin, Stochastic process leading to wave equations in dimensions higher than one, Phys. Rev. E 81 (2010), 0211131–5.10.1103/PhysRevE.81.021113Search in Google Scholar PubMed
[16] A. D. Kolesnik and M. A. Pinsky, Random evolutions are driven by hyperparabolic operators, J. Stat. Phys. 142 (2011), 828–846.10.1007/s10955-011-0131-0Search in Google Scholar
[17] G. Doolen, U. Frisch, B. Hasslacher, S. Orszag and S. Wolfram (eds.), Lattice Gas Methods for Partial Differential Equations, Addison-Wesley, Menlo Park, 1990.Search in Google Scholar
[18] M. M. Alvarez, F. J. Muzzio, S. Cerbelli, A. Adrover and M. Giona, Self-similar spatiotemporal structure of intermaterial boundaries in chaotic flows. Phys. Rev. Lett. 81 (1998), 3395–3398.10.1103/PhysRevLett.81.3395Search in Google Scholar
©2016 by De Gruyter Mouton