Related papers: Early-Warning Signs for SPDEs with Continuous Spec…
The computer algebra routines documented here empower you to reproduce and check many of the details described by an article on large deviations for slow-fast stochastic systems [abs:1001.4826]. We consider a 'small' spatial domain with two…
Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of…
In this paper, we report a theoretical study of the phase diffusion in a gain-switched single-mode semiconductor laser. We use stochastic rate equations for the electrical field to analyze the phase statistics of the gain-switched laser.…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
This paper studies stabilities of stochastic differential equation (SDE) driven by time-changed L\'evy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics,…
We analyze the strong noise limit of one-dimensional stochastic differential equations (SDEs). Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs,…
The use of critical slowing down as an early warning indicator for regime switching in observations from stochastic environments and noisy dynamical models has been widely studied and implemented in recent years. Some systems, however, have…
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…
In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and nonlinear high-order SPDEs driven by time-dependent Wiener…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…