Related papers: Effective Filtering for Multiscale Stochastic Dyna…

In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…

This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by L\'evy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a…

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales.…

We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. Firstly, we prove that the dimension for the signal system can be reduced by a homogenized approach. Secondly,…

This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow…

This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…

We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…

We develop algorithms for computing expectations of the laws of models associated to stochastic differential equations (SDEs) driven by pure L\'evy processes. We consider filtering such processes and well as pricing of path dependent…

Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

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…

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…

This work concerns the nonlinear filtering problem of multiscale McKean-Vlasov stochastic systems where the whole systems depend on distributions of fast components. First of all, we prove that the slow component of the original system…

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…