Related papers: Some Large Deviations Asymptotics in Small Noise F…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…
This paper is devoted to investigating the Freidlin-Wentzell's large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
We demonstrate the large deviation principle in the small noise limit for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation. In this paper, we first prove the well-posedness of weak solutions…
We obtain a large deviation principle describing the small time asymptotics of the solution of a stochastic evolution equation with multiplicative noise. Our assumptions are a condition on the linear drift operator that is satisfied by…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise…
In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear…
The initial-value problem for the drift-diffusion equation arising from the model of semiconductor device simulations is studied. The dissipation on this equation is given by the fractional Laplacian. When the exponent of the fractional…
We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
We consider a controlled second order differential equation which is partially observed with an additional fractional noise. we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of…
This thesis is devoted to the study of ergodicity and large deviations for the stochastic nonlinear wave (NLW) equation with smooth white noise in 3D. Under some standard growth and dissipativity assumptions on the nonlinearity, we show…
For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…
We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\Z^d$ in the spirit of Donsker-Varadhan \cite{DV75}. We work in the interesting…
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we…
In this paper, we focus on two kinds of large deviations principles (LDPs) of the invariant measures of Langevin equations and their numerical methods, as the noise intensity $\epsilon\to 0$ and the dissipation intensity $\nu\to\infty$…
In this paper, we establish a small time large deviation principle (small time asymptotics) for the dynamical $\Phi^4_1$ model, which not only involves study of the space-time white noise with intensity $\sqrt{\varepsilon}$, but also the…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…