In financial and actuarial modeling and other areas of application, stochastic differential
equations with jumps have been employed to describe the dynamics of various state …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

We present a unified framework to analyze the global convergence of Langevin dynamics
based algorithms for nonconvex finite-sum optimization with $ n $ component functions. At …

Stochastic differential equations (SDEs) represent physical phenomena dominated by
stochastic processes. As for deterministic ordinary differential equations (ODEs), various …

Abstract “Backward” Lagrangian stochastic models calculate an ensemble of fluid element
(particle) trajectories that are distinguished by each passing through an observation point …

This paper aims to give an overview and summary of numerical methods for the solution of
stochastic differential equations. It covers discrete time strong and weak approximation …

This paper introduces some implicitness in stochastic terms of numerical methods for solving
stiff stochastic differential equations and especially aclass of fully implicit methods, the …

A framework for creating and updating digital twins for dynamical systems from a library of
physics-based functions is proposed. The sparse Bayesian machine learning is used to …

Extracting governing physics from data is a key challenge in many areas of science and
technology. The existing techniques for equation discovery are mostly applicable to …

In this paper, a stochastic SIS epidemic model with nonlinear incidence rate and double
epidemic hypothesis is proposed and analysed. We explain the effects of stochastic …