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