相关论文: Noise corrections to stochastic trace formulas

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 extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix…

We use a model based on the fractional Langevin equation with external noise to describe the anomalous dynamics observed in microrheology experiments in living cells. This model reproduces both the subdiffusive short-time and the…

Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…

In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…

We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for…

Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps.…

We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…

This work is devoted to quantifying how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit expression for approximating the rate change is provided,…

We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the…

We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…

In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain $\Omega\subset\dR^n$ with smooth compact boundary are studied. A Schatten--von Neumann type…

Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…

This paper is a survey of recent results on the adaptive robust non parametric methods for the continuous time regression model with the semi - martingale noises with jumps. The noises are modeled by the L\'evy processes, the Ornstein --…

The transition density of a stochastic, logistic population growth model with multiplicative intrinsic noise is analytically intractable. Inferring model parameter values by fitting such stochastic differential equation (SDE) models to data…

We study the most probable trajectories of the concentration evolution for the transcription factor activator in a genetic regulation system, with non-Gaussian stable L\'evy noise in the synthesis reaction rate taking into account. We…

We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a…

A time-discrete approach avoids the assumption of an 'integration sense'. New path increments (in a short time step) are complete in the order of that step, and not Gaussian distributed when the noise is multiplicative; this eliminates an…