On a class of exponential changes of measure for stochastic PDEs

Given a mild solution X to a semilinear stochastic partial differential equation (SPDE), we consider an exponential change of measure based on its infinitesimal generator L, defined in the topology of bounded pointwise convergence. The changed measure P^h depends on the choice of a function h in the domain of L. In our main result, we derive conditions on h for which the change of measure is of Girsanov-type. The process X under P^h is then shown to be a mild solution to another SPDE with an extra additive drift-term. We illustrate how different choices of h impact the law of X under P^h in selected applications. These include the derivation of an infinite-dimensional diffusion bridge as well as the introduction of guided processes for SPDEs, generalizing results known for finite-dimensional diffusion processes to the infinite-dimensional case.