On the Solutions of Non Linear Stochastic Fractional Partial Differential Equations in One Spatial Dimension

Latifa Debbi (1) , Marco Dozzi (1)

1 IECN - Institut Élie Cartan de Nancy

Existence, uniqueness and regularity of the trajectories of mild solutions of one-dimensional non linear stochastic fractional partial differential equations of order $\alpha >1 $ containing derivatives of entire order and perturbed by space-time white noise are studied. The fractional derivative operator is defined by means of a generalized Riesz-Feller potential.

Mots clés: fractional derivative operator; stochastic partial differential equation; space-time white noise; H{ö}lder continuity; equation of high order

Domaines: Probabilités [math.PR]

Latifa Debbi, Marco Dozzi. On the Solutions of Non Linear Stochastic Fractional Partial Differential Equations in One Spatial Dimension. Stochastic Processes and their Applications, 2005, 115, pp.1764--1781. ⟨hal-00144121⟩