The 1-d stochastic wave equation driven by a fractional Brownian motion

Abstract

In this paper, we develop a Young integration theory in dimension 2 which will allow us to solve a non-linear one dimensional wave equation driven by an arbitrary signal whose rectangular increments satisfy some H\"{o}lder regularity conditions, for some H\"older exponent greater than 1/2. This result will be applied to the infinite dimensional fractional Brownian motion.Comment: 37 pages, 3 figure