Related papers: Large deviations for the one-dimensional Edwards m…
We consider the problem of optimally stopping a general one-dimensional stochastic differential equation (SDE) with generalised drift over an infinite time horizon. First, we derive a complete characterisation of the solution to this…
In this paper, we study a large deviation principle for the solution of a backward stochastic differential equation driven by $G$-Brownian motion with subdifferential operator.
We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give explicit upper and lower bounds for the rate function of the…
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…
We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…
In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential…
Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $\sigma:\rr^d\to…
It is well known that the Euler-Maruyama discretisation of an autonomous SDE using a uniform timestep $h$ has a strong convergence error which is $O(h^{1/2})$ when the drift and diffusion are both globally Lipschitz. This note proves that…
We derive an annealed large deviation principle (LDP) for the normalised and rescaled local times of a continuous-time random walk among random conductances (RWRC) in a time-dependent, growing box in $\Z^d$. We work in the interesting case…
We study the radius $R_T$ of a self-repellent fractional Brownian motion $\left\{B^H_t\right\}_{0\le t\le T}$ taking values in $\mathbb{R}^d$. Our sharpest result is for $d=1$, where we find that with high probability, \begin{equation*} R_T…
We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…
Given a standard Brownian motion $B^{\mu}=(B_t^{\mu})_{0\le t\le T}$ with drift $\mu \in \mathbb{R}$ and letting $S_t^{\mu}=\max_{0\le s\le t}B_s^{\mu}$ for $0\le t\le T$, we consider the optimal prediction problem: \[V=\inf_{0\le \tau \le…
In this note, we prove the Freidlin-Wentzell's large deviation principle for BSDEs with one-sided reflection.
This work establishes a large deviation principle for the spectral measure of the Lax matrix associated to the periodic Toda chain of $N$ particles, subject to a generalised Gibbs measure. This large deviation principle is governed by a…
We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times of the infimum and the supremum before the…
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…