Related papers: Stochastic Evolution Equations of Jump Type with R…
In the paper, a class of second-order McKean-Vlasov stochastic evolution equation driven by Poisson jumps with non-Lipschitz conditions is considered. The existence and uniqueness of the mild solution is established by means of the…
This work establishes two versions of the Pontryagin-type maximum principles for partially observed optimal control of coupled forward stochastic partial differential equations (FSPDEs) and backward stochastic differential equations (BSDEs)…
In this paper, we study a stochastic linear-quadratic control problem with random coefficients and regime switching on a horizon $[0,T\wedge\tau]$, where $\tau$ is a given random jump time for the underlying state process and $T$ is a…
We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
The aim of this paper is to establish the existence and uniqueness of the solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our system is Markovian in the sense…
A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…
The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…
An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic…
In this paper we derive for a controlled stochastic evolution system on a Hilbert space sufficient conditions for optimality. Our result is derived by using its so-called adjoint backward stochastic evolution equation.
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
In the paper, we consider the no-explosion condition and pathwise uniqueness for SDEs driven by a Poisson random measure with coefficients that are super-linear and non-Lipschitz. We give a comparison theorem in the one-dimensional case…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The…
The paper is devoted to a stochastic optimal control problem for a two scale, infinite dimensional, stochastic system. The state of the system consists of slow and fast component and its evolution is driven by both continuous Wiener noises…
In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison…
A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…
We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…