57 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
Optimal Stopping Under Model Uncertainty in a General Setting
We consider the optimal stopping time problem under model uncertainty , for every stopping time , set in the framework of families
of random variables indexed by stopping times. This setting is more general
than the classical setup of stochastic processes, and particularly allows for
general payoff processes that are not necessarily right-continuous. Under
weaker integrability, and regularity assumptions on the reward family , we show the existence of an optimal stopping time. We then
proceed to find sufficient conditions for the existence of an optimal model.
For this purpose, we present a universal Doob-Meyer-Mertens's decomposition for
the Snell envelope family associated with in the sense that it holds
simultaneously for all . This decomposition is then
employed to prove the existence of an optimal probability model and study its
properties
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