Related papers: A large deviation principle for the normalized exc…
We prove that bridges of subelliptic diffusions on a compact manifold, with distinct ends, satisfy a large deviation principle in a space of Holder continuous functions, with a good rate function, when the travel time tends to 0. This leads…
We consider Kallenberg's hypothesis on the characteristic function of a L\'{e}vy process and show that it allows the construction of weakly continuous bridges of the L\'{e}vy process conditioned to stay positive. We therefore provide a…
In this paper, we show a large deviation principle for certain sequences of static Schr\"{o}dinger bridges, typically motivated by a scale-parameter decreasing towards zero, extending existing large deviation results to cover a wider range…
Recent fluctuation identities for $\alpha$-stable L\'evy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
In this paper we investigate the asymptotic properties of the wait-first and jump-first L\'evy walk with rest, which is a generalization of standard jump-first and jump-first L\'evy walk that assumes each waiting time in the model is a sum…
We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…
Generalized Large deviation principles was developed for Colombeau-Ito SDE with a random coefficients. We is significantly expand the classical theory of large deviations for randomly perturbed dynamical systems developed by Freidlin and…
This paper addresses heavy-tailed large deviation estimates for the distribution tail of functionals of a class of spectrally one-sided L\'evy process. Our contribution is to show that these estimates remain valid in a near-critical regime.…
The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.
In this article, we introduce an infinite-dimensional analogue of the $\alpha$-stable L\'evy motion, defined as a L\'evy process $Z=\{Z(t)\}_{t \geq 0}$ with values in the space $\mathbb{D}$ of c\`adl\`ag functions on $[0,1]$, equipped with…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the…
We investigate periodic points of the Dyck shift from the viewpoint of large deviations. We establish the level-2 Large Deviation Principle with the rate function given in terms of Kolmogorov-Sinai entropies of shift-invariant Borel…
Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \infty] $ such that, for all $\alpha \in…
We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous…
The characteristic measure of excursions away from a regular point is studied for a class of symmetric L\'evy processes without Gaussian part. It is proved that the harmonic transform of the killed process enjoys Feller property. The result…
As a generalization of scale functions of spectrally negative L\'evy processes, we define scale functions of general standard processes with no positive jumps. For this purpose, we utilize excursion measures. Using our new scale functions…
Starting with the large deviation principle (LDP) for the Erd\H{o}s-R\'enyi binomial random graph $\mathcal{G}(n,p)$ (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the LDP for the uniform random graph…
We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and…