Related papers: Trace asymptotics for subordinate semigroups

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 study Brownian motion in a drifted Brownian potential in the subexponential regime. We prove that the annealed probability of deviating below the almost sure speed has a polynomial rate of decay and compute the exponent in this power…

In this paper, we consider transient subordinate Brownian motion X in R^d, d \geq 1, where the Laplace exponent \phi of the corresponding subordinator satisfies some mild conditions. The scaleinvariant Harnack inequality is proved for X. We…

The infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length $T$ around a fixed origin when $T \rightarrow +\infty$. The aim of this note is to study its long-time asymptotics on…

We study the asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time Z_t:= X_{Y_t}, t >= 0, where X is a fractional Brownian motion and Y is an independent Brownian motion.

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon\to0$.

In this paper, we study the asymptotic behavior, as the time $t$ goes to zero, of the trace of the semigroup of a killed relativistic $\alpha$-stable process in bounded $C^{1,1}$ open sets and bounded Lipschitz open sets. More precisely, we…

This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be…

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…

We give short proofs of two classical results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour.

We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than…

In this paper we investigate the class of grey Brownian motions $B_{\alpha,\beta}$ ($0<\alpha<2$, $0<\beta\leq1$). We show that grey Brownian motion admits different representations in terms of certain known processes, such as fractional…

We establish a small time large deviation principle and a Varadhan type asymptotics for Brownian motion with singular drift on $\bR^d$ with $d\geq 3$ whose infinitesimal generator is $\frac12 \Delta + \mu \cdot \nabla$, where each $\mu_i$…

The signature of a path \gamma is a sequence whose n-th term is the order-n iterated integrals of \gamma. It arises from solving multidimensional linear differential equations driven by \gamma. We are interested in relating the path…

We investigate the asymptotic disconnection time of a large discrete cylinder $(\mathbb{Z}/N\mathbb{Z})^{d}\times \mathbb{Z}$, $d\geq 2$, by simple and biased random walks. For simple random walk, we derive a sharp asymptotic lower bound…

We prove a conjecture of Broadurst (arXiv:1004.0519v1) on asymptotic expansions of certain polylogarithm type functions related to the Dickman function.

We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $\mathbb R\times \mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov…

We consider parameterized exponential integrals coming from the time evolution of the probability distribution of Brownian motion on globally subanalytic sets. We establish definability results and asymptotic expansions.

Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then…

This paper proves an analogue of a result of Banuelos and Sa Barreto on the asymptotic expansion for the trace of Schrodinger operators on $\R^d$ when the Laplacian $\Delta$, which is the generator of the Brownian motion, is replaced by the…