A new volume of philosophical essays by Bernard Williams. The book is a successor to
Problems of the Self, but whereas that volume dealt mainly with questions of personal …

In this paper, we introduce a numerical method for nonlinear parabolic partial differential
equations (PDEs) that combines operator splitting with deep learning. It divides the PDE …

These lectures will concentrate on (nonlinear) stochastic partial differential equations
(SPDEs) of evolutionary type. All kinds of dynamics with stochastic influence in nature or …

Second order linear parabolic and elliptic equations arise frequently in mathematics and
other disciplines. For example parabolic equations are to be found in statistical mechanics …

We investigate well-posedness for martingale solutions of stochastic differential equations,
under low regularity assumptions on their coefficients, widely extending the results first …

Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the
most popular and flexible tools for sampling high-dimensional probability measures. Non …

The celebrated Hörmander condition is a sufficient (and nearly necessary) condition for a
second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients …

We present a generalization of Krylov–Rozovskii's result on the existence and uniqueness of
solutions to monotone stochastic differential equations. As an application, the stochastic …

Consider the metric space (P 2 (R d), W 2) of square integrable laws on R d with the
topology induced by the 2-Wasserstein distance W 2. Let Φ: P 2 (R d)→ R and μ∈ P 2 (R d) …

This paper is concerned with the numerical approximation of stochastic ordinary differential
equations, which satisfy a global monotonicity condition. This condition includes several …