Related papers: Stochastic Evolution Equation Driven by Teugels Ma…
In this work, we prove a version of H\"{o}rmander's theorem for a stochastic evolution equation driven by a trace-class fractional Brownian motion with Hurst exponent $\frac{1}{2} < H < 1$ and an analytic semigroup on a given separable…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…
In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An…
In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier-Stokes system. Looking for sparsity, we take controls as functions of time taking values in a space of Borel measures. The cost functional…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework is given as an abstract "martingale formulation", which…
We present an existence theory for martingale and strong solutions to doubly nonlinear evolution equations in a separable Hilbert space in the form $$d(Au) + Bu\,dt \ni F(u)\,dt + G(u)\,dW$$ where both $A$ and $B$ are maximal monotone…
We prove maximal $L^p$-regularity for the stochastic evolution equation \[\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}.\] under the assumption that $A$ is a sectorial…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
We present a control model for an octopus tentacle, based on the dynamics of an inextensible string with curvature constraints and curvature controls. We derive the equations of motion together with an appropriate set of boundary…
In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by L\'evy process consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
The main purpose of this paper is to give a solution to a long-standing unsolved problem in stochastic control theory, i.e., to establish the Pontryagin-type maximum principle for optimal controls of general infinite dimensional nonlinear…
We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such problem has been the object of various papers in deterministic cases when the possible…
By extending \cite{bensoussan2015control}, we implement the proposal of Lions \cite{lions14} on studying mean field games and their master equations via certain control problems on the Hilbert space of square integrable random variables. In…
We study an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…