The 1-d stochastic wave equation driven by a fractional Brownian sheet Lluıs Quer-Sardanyons ? Project OMEGA, INRIA Lorraine Institut Elie Cartan, Campus Scientifique BP 239 – 54506 Vandœuvre-les-Nancy, France Samy Tindel Institut Elie Cartan, Universite de Nancy 1 BP 239 – 54506 Vandœuvre-les-Nancy, France 29th January 2007 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 Holder regularity conditions, for some Holder exponent greater than 1/2. This result will be applied to the fractional Brownian sheet. Keywords: wave equation, fractional Brownian sheet, Young integration. MSC: 60H15, 60G15, 35L05 ?Supported by an INRIA's Postdoc grant and grants BFM2003-01345 and HF2003-006, Direccion General de Investigacion, Ministerio de Educacion y Ciencia, Spain. 1
- young integral
- dimensional wave
- noise has
- been considered
- holder exponent
- positive real constant
- equation driven
- stochastic differential equations
- brownian noise
- brownian sheet