Fractional elliptic, hyperbolic and parabolic random fields. (English) Zbl 1231.60045

Leonenko, Nikolai; Ruiz-Medina, María D.; Taqqu, Murad S.

Electron. J. Probab. 16, Paper No. 40, 1134-1172 (2011).

Summary: New classes of fractional and multi-fractional random fields arising from elliptic, parabolic and hyperbolic equations with random innovations derived from a fractional Brownian motion are introduced. The case of stationary random initial conditions is also considered for parabolic and hyperbolic equations.

MSC:

60G60	Random fields
60G18	Self-similar stochastic processes
60G20	Generalized stochastic processes
60G22	Fractional processes, including fractional Brownian motion
35J15	Second-order elliptic equations
35K10	Second-order parabolic equations
35L10	Second-order hyperbolic equations

Keywords:

cylindrical fractional Brownian motion; elliptic, hyperbolic, parabolic random fields; fractional Bessel potential spaces; fractional Hölder spaces; fractional random fields; multi-fractional random fields; spectral representation