The stochastic nonlinear heat equation

This thesis considers a stochastic partial differential equation which may be viewed as a stochastic version of the nonlinear heat equation studied by Eells and Sampson. The special case of loops on a compact Riemannian manifold M is studied, where the loop is parametrised by the unit circle. Using ideas of Eells and Sampson and the theory of stochastic evolution equations on infinite dimensional M-type 2 Banach spaces, existence and uniqueness of an M-valued solution is shown, where M is a certain Sobolev-Slobodetski space of loops on the manifold M. In particular M is an infinite dimensional manifold modelled on an M-type 2 Banach space.Finally, an approximation result of the Wong-Zakai type for Stratonovich integrals in M-type 2 Banach spaces is given