Related papers: Stable limit theorems for additive functionals of …
This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $\alpha$-stable process.
We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic…
In this article, we study fluctuations of the volume of a stable sausage defined via a $d$-dimensional rotationally invariant $\alpha$-stable process. As the main results, we establish a functional central limit theorem (in the case when…
We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…
We prove a functional non-central limit theorem for jump-diffusions with periodic coefficients driven by strictly stable Levy-processes with stability index bigger than one. The limit process turns out to be a strictly stable Levy process…
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…
We study a general limiting framework for the convergence of sequences of additive functionals of diffusions to L\'evy subordinators, and provide explicit sufficient conditions that both ensure convergence and characterize the law of the…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…
We study anomalous diffusion for one-dimensional systems described by a generalized Langevin equation. We show that superdiffusion can be classified in slow superdiffusion and fast superdiffusion. For fast superdiffusion we prove that the…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…
We establish multidimensional analogues of one-dimensional stable limit theorems due to H\"ausler and Luschgy (2015) for so called explosive processes. As special cases we present multidimensional stable limit theorems involving…
Fox's H-function provide a unified and elegant framework to tackle several physical phenomena. We solve the space fractional diffusion equation on the real line equipped with a delta distribution initial condition and identify the…
A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A…