Related papers: Improved order 1/4 convergence for piecewise const…
This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…
In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using PS methods. It is a first proved convergence rate in the literature of PS optimal control. In addition to the high-order convergence rate, two…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
Time-stepping $hp$-versions discontinuous Galerkin (DG) methods for the numerical solution of fractional subdiffusion problems of order $-\alpha$ with $-1<\alpha<0$ will be proposed and analyzed. Generic $hp$-version error estimates are…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
We prove a rate of convergence for the $N$-particle approximation of a second-order partial differential equation in the space of probability measures, like the Master equation or Bellman equation of mean-field control problem under common…
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method developed also provided an overapproximation of the reachable…
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new…
This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems,…
We determine the convergence speed of a numerical scheme for approximating one-dimensional continuous strong Markov processes. The scheme is based on the construction of coin tossing Markov chains whose laws can be embedded into the process…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
We analyse a version of the policy iteration algorithm for the discounted infinite-horizon problem for controlled multidimensional diffusion processes, where both the drift and the diffusion coefficient can be controlled. We prove that,…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…