Related papers: Stochastic averaging lemmas for kinetic equations
The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such…
The problem of time in canonical quantum gravity remains one of the most significant challenges, primarily due to the "frozen" formalism emerging from the Wheeler-DeWitt equation. Within the ADM formalism, we introduce a novel approach in…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
We introduce a stochastic version of Gubinelli's sewing lemma, providing a sufficient condition for the convergence in moments of some random Riemann sums. Compared with the deterministic sewing lemma, adaptiveness is required and the…
We formulate a class of stochastic partial differential equations based on Kelvin's circulation theorem for ideal fluids. In these models, the velocity field is randomly transported by white-noise vector fields, as well as by its own…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and uniqueness of invariant measures are established for…
We revisit aspects of dynamics and stability of localized states in the deterministic and stochastic discrete nonlinear Schr\"odinger equation. By a combination of analytic and numerical techniques, we show that localized initial conditions…
The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into…
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,…
In this paper we establish a substitution formula for stochastic differential equation driven by generalized grey noise. We then apply this formula to investigate the absolute continuity of the solution with respect to the Lebesgue measure…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physical description of irreversibility at the field-theoretic…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
Our first result is a stochastic sewing lemma with quantitative estimates for mild incremental processes, with which we study SPDEs driven by fractional Brownian motions in a random environment. We obtain uniform $L^p$-bounds. Our second…
We consider in this paper travelling wave solutions to stochastic partial differential equations and corresponding wave speed. As a particular example we consider the Nagumo equation with multiplicative noise which we mainly consider in the…