Related papers: Some stochastic process techniques applied to dete…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
Background. It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…
This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
This tutorial teaches parts of the finite element method (FEM), and solves a stochastic partial differential equation (SPDE). The contents herein are considered "known" in the numerics literature, but for statisticians it is very difficult…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…