Related papers: Delay-dependent Asymptotic Stability of Highly Non…
This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…
Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
This paper develops methods for numerically solving stochastic delay-differential equations (SDDEs) with multiple fixed delays that do not align with a uniform time mesh. We focus on numerical schemes of strong convergence orders $1/2$ and…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We consider a class of time-inhomogeneous optimal stopping problems and we provide sufficient conditions on the data of the problem that guarantee monotonicity of the optimal stopping boundary. In our setting, time-inhomogeneity stems not…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay…
We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators. Two methods, i.e., the penalization method and the Picard…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. We deal with linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation…