Related papers: Local time of Levy random walks: a path integral a…

Following our previous work [68], this paper continues to investigate the evolution dynamics of local times of spectrally positive L\'evy processes with Gaussian components in the spatial direction. We prove that conditioned on the…

In this work, we generalise the stochastic local time space integration introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove…

In this paper, we study a transient spatially inhomogeneous random walk with asymptotically zero drifts on the lattice of the positive half line. We give criteria for the finiteness of the number of points having exactly the same local time…

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…

We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…

In present paper we prove an existence and give a moments estimate for the local time of Gaussian integrators. Every Gaussian integrator is associated with a continuous linear operator in the space of square integrable functions via white…

Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…

For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the L\'evy measure of the inverse local time is subexponential…

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…

In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…

We study the penalization problem with various clocks where the weight is given as the exponential functional of multi-point local times for one-dimensional L\'{e}vy processes. The limit processes may vary according to the choice of random…

We study the convergence in distribution of the supremum of the local time and of the favorite site for a transient diffusion in a spectrally negative L\'evy potential. To do so, we study the h-valleys of a spectrally negative L\'evy…

This paper is concerned with the evolution dynamics of local times of a spectrally positive stable process in the spatial direction. The main results state that conditioned on the finiteness of the first time at which the local time at zero…

Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical…

The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean-Vlasov (mean-field) stochastic differential equation. If the Donsker delta measure is absolutely…

We establish the consistency of a local time approximation of a diffusion at a sticky threshold based on high-frequency observations. First, we prove the result for sticky Brownian motion, and then extend it to It\^o diffusions with a…

We study the upper tail behaviors of the local times of the additive L\'{e}vy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L_2-norms of the…