Related papers: A control variate method based on polynomial appro…
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…
We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
The aim of this paper is to describe a new an integrated methodology for project control under uncertainty. This proposal is based on Earned Value Methodology and risk analysis and presents several refinements to previous methodologies.…
We deal with the problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latters being characterized by…
We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to…
We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients,…
In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
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…
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete quadratic variation process. One basis of this is a similar…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…
This paper deals with asymptotic errors, limit theorems for errors between numerical and exact solutions of stochastic differential equation (SDE) driven by one-dimensional fractional Brownian motion (fBm). The Euler-Maruyama, higher-order…
A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalised. The novel…
This paper proposes to parameterize open loop controls in stochastic optimal control problems via suitable classes of functionals depending on the driver's path signature, a concept adopted from rough path integration theory. We rigorously…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…
We consider the pricing and the sensitivity calculation of continuously monitored barrier options. Standard Monte Carlo algorithms work well for pricing these options. Therefore they do not behave stable with respect to numerical…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…