Related papers: On the study of slow-fast dynamics, when the fast …
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…
We study Markov population processes on large graphs, with the local state transition rates of a single vertex being linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
The stability of dynamical systems with oscillatory behaviors and well-defined average vector fields has traditionally been studied using averaging theory. These tools have also been applied to hybrid dynamical systems, which combine…
We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…
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 propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
We show a decomposition into the sum of a martingale and a deterministic quantity for time averages of the solutions to non-autonomous SDEs and for discrete-time Markov processes. In the SDE case the martingale has an explicit…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…
We introduce and analyze a novel class of inverse problems for stochastic dynamics: Given the ergodic invariant measure of a stochastic process governed by a nonlinear stochastic ordinary or partial differential equation (SODE or SPDE), we…
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…
Collective motion is an ubiquitous phenomenon in nature, inspiring engineers, physicists and mathematicians to develop mathematical models and bio-inspired designs. Collective motion at small to medium group sizes ($\sim$10-1000…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…