We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional space X, it takes values in the positive cone...

In this paper we construct the smallest semigroup S that dominates a given family of linear Feller semigroups. The semigroup S will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong continuity properties of the semigroup envelope and show that it...

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let (D,M,μ) be a finite measure space and consider the Hilbert space...

We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional space X, it takes values in the positive cone...

In this paper we construct the smallest semigroup S that dominates a given family of linear Feller semigroups. The semigroup S will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong continuity properties of the semigroup envelope and show that it...

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let (D, M, μ) be a finite measure space and consider the Hilbert space H...

We present a general framework for solving stochastic porous medium equations and stochastic Navier-Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion...