56 research outputs found
Singular control of SPDEs with space-mean dynamics
We consider the problem of optimal singular control of a stochastic partial
differential equation (SPDE) with space-mean dependence. Such systems are
proposed as models for population growth in a random environment. We obtain
sufficient and necessary maximum principles for such control problems. The
corresponding adjoint equation is a reflected backward stochastic partial
differential equation (BSPDE) with space-mean dependence. We prove existence
and uniqueness results for such equations. As an application we study optimal
harvesting from a population modelled as an SPDE with space-mean dependence.Comment: arXiv admin note: text overlap with arXiv:1807.0730
Estimates Uniform in Time for the Transition Probability of Diffusions with Small Drift and for Stochastically Perturbed Newton Equations
An estimate uniform in time for the transition probability of diffusion processes with small drift is given. This also covers the case of a degenerate diffusion describing a stochastic perturbation of a particle moving according to the Newton's law. Moreover the random wave operator for such a particle is described and the analogue of asymptotic completeness is proven, the latter in the case of a sufficiently small drif
- …