Related papers: Deep BSVIEs Parametrization and Learning-Based App…
Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
By using the Skorohod equation we derive an iteration procedure which allows us to solve a class of reflected backward stochastic differential equations with non-linear resistance induced by the reflected local time. In particular, we…
Stochastic Volterra integral equations with jumps (SVIEs) have become very common and widely used in numerous branches of science, due to their connections with mathematical finance, biology, engineering and so on. In this paper, we apply…
We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure. We focus on problems where calculating the posterior distribution is…
This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
In this paper, we consider dynamic risk measures induced by backward stochastic differential equations (BSDEs). We discuss different examples that come up in the literature, including the entropic risk measure and the risk measure arising…
In this paper, we consider a class of backward doubly stochastic differential equations (BDSDE for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both…
Variational autoencoder (VAE) is a deep generative model for unsupervised learning, allowing to encode observations into the meaningful latent space. VAE is prone to catastrophic forgetting when tasks arrive sequentially, and only the data…
This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a…
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the…
In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first…
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and…
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…
We address the optimal control of stochastic Volterra integral equations with delay through the lens of Hida-Malliavin calculus. We show that the corresponding adjoint processes satisfy an anticipated backward stochastic Volterra integral…
We study backward stochastic difference equations (BS{\Delta}E) driven by a d-dimensional stochastic process on a lattice whose increments have only d + 1 possible values that generates the lattice. Regarding the driving process as a d…