Related papers: A Large Deviation Principle for Martingales over B…
In this paper, a probabilistic interpretation for the viscosity solution of a parabolic partial differential equation is obtained by virtue of the solution of a class of quadratic backward stochastic differential equations (BSDEs, for…
In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. a…
We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\sigma$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the…
We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with Dirichlet boundary condition. We consider the case that the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon}…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
When a Brownian motion is scaled according to the law of the iterated logarithm, its supremum converges to one as time tends to zero. Upper large deviations of the supremum process can be quantified by writing the problem in terms of…
We continue the investigation of the spectral theory and exponential asymptotics of Markov processes, following Kontoyiannis and Meyn (2003). We introduce a new family of nonlinear Lyapunov drift criteria, characterizing distinct subclasses…
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao and Liu \cite{GL}, this extends the corresponding results collected in…
In this paper, we consider the large deviations principles (LDPs) for the stochastic linear Schr\"odinger equation and its symplectic discretizations. These numerical discretizations are the spatial semi-discretization based on spectral…
Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions $\mathscr L$ that induce a flow, given by $\mathscr L(\rho_t,\dot\rho_t)=0$. We derive necessary and…
We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.
This work concerns about stochastic Burgers type equations with reflection. First of all, by means of the equicontinuous uniform Laplace principle, we prove the Freidlin-Wentzell uniform large deviation principle for these equations…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…
Let $A_N$ be distributed according to the Haar probability measure on the orthogonal group $\mathscr{O}(N)$ for each $N\in\mathbb{N}$. It is well-known that the upper left $m_N\times k_N$ block of $\sqrt{N}A_N$ with $m_Nk_N = o(N)$…
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
Consider an intersection measure $\ell_t ^{\mathrm{IS}}$ of $p$ independent (possibly different) $m$-symmetric Hunt processes up to time $t$ in a metric measure space $E$ with a Radon measure $m$. We derive a Donsker-Varadhan type large…