Related papers: Stochastic differential equations with a fractiona…
We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown It\^o process, the proposed…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the process…
The paper studies solutions of stochastic partial differential equations with random initial conditions. First, it overviews some of the known results on scaled solutions of such equations and provides several explicit motivating examples.…
Accurate risk assessment is essential for safety-critical autonomous and control systems under uncertainty. In many real-world settings, stochastic dynamics exhibit asymmetric jumps and long-range memory, making long-term risk probabilities…
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…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
We consider several models of State Dependent Delay Differential Equations (SDDEs), in which the delay is affected by a small parameter. This is a very singular perturbation since the nature of the equation changes. Under some conditions,…
We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…
We discuss a class of Backward Stochastic Differential Equations(BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be associated…
This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-dependent we mean that the coefficients of the…
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…
Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…
Energy-efficient real-time task scheduling has been actively explored in the past decade. Different from the past work, this paper considers schedulability conditions for stochastic real-time tasks. A schedulability condition is first…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…