相关论文: Non-Boltzmann Equilibrium Probability Densities fo…
We propose non-asymptotic controls of the cumulative distribution function $P(|X_{t}|\ge \varepsilon)$, for any $t>0$, $\varepsilon>0$ and any L\'evy process $X$ such that its L\'evy density is bounded from above by the density of an…
We consider a type of stochastic nonlinear beam equation driven by L\'{e}vy noise. By using a suitable Lyapunov function and applying the Khasminskii test we show the nonexplosion of the mild solutions. In addition, under some additional…
In this paper, we study the existence of the density associated to the exponential functional of the L\'evy process $\xi$, \[ I_{\ee_q}:=\int_0^{\ee_q} e^{\xi_s} \, \mathrm{d}s, \] where $\ee_q$ is an independent exponential r.v. with…
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on $\mathbb{R} ^d$ under the assumption that its L\'{e}vy--Khintchine exponent varies slowly. We also derive…
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which…
In this paper nonparametric methods to assess the multivariate L\'{e}vy measure are introduced. Starting from high-frequency observations of a L\'{e}vy process $\mathbf{X}$, we construct estimators for its tail integrals and the…
We study the asymptotic behavior of the emptiness formation probability for large spin strings in a translation invariant quasifree nonequilibrium steady state of the isotropic XY chain. Besides the overall exponential decay, we prove that,…
We study the fractional three-dimensional (3D) nonlinear Schr\"{o}dinger equation with exponential saturating nonlinearity. In the case of the L\'{e}vy index $\alpha=1.9$, this equation can be considered as a model equation to describe…
We prove several necessary and sufficient conditions for the existence of (smooth) transition probability densities for L\'evy processes and isotropic L\'evy processes. Under some mild conditions on the characteristic exponent we calculate…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
The periodic homogenization problem of integro-differential equations of the alpha stable L{\'e}vy operators is studied in this paper. Thanking to the symmetry of the L{\'e}vy density, we can use the method of the formal asymptotic…
We study the barrier crossing of a particle driven by white symmetric Levy noise of index $\alpha$ and intensity $DD for three different generic types of potentials: (a) a bistable potential; (b) a metastable potential; and (c) a truncated…
We consider the Schroedinger equation with a supersymmetric random potential, where the superpotential is a Levy noise. We focus on the problem of computing the so-called complex Lyapunov exponent, whose real and imaginary parts are,…
We consider periodic homogenization problems for the L{\'e}vy operators with asymmetric L{\'e}vy densities. The formal asymptotic expansion used for the $\a$-stable (symmetric) L{\'e}vy operators ($\a\in (0,2)$) is not applicable directly…
We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight $e^{-nV(\cos x)}$, assuming that the potential $V$ has four bounded derivatives on $[-1,1]$ and the…
This work describes the effects of L\'evy noise on a birhythmic van der Pol like oscillator. Numerical simulations demonstrate that the noise induced escapes from an attractor to another are not markedly different from escapes between…
We analyze two-dimensional (2D) random systems driven by a symmetric L\'{e}vy stable noise which, under the sole influence of external (force) potentials $\Phi (x) $, asymptotically set down at Boltzmann-type thermal equilibria. Such…
We study the probability distribution function (pdf) of the position of a L\'evy flight of index 0<\alpha<2 in presence of an absorbing wall at the origin. The solution of the associated fractional Fokker-Planck equation can be constructed…
In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic L\'evy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise…
In this paper we present some limit theorems for power variation of L\'evy semi-stationary processes in the setting of infill asymptotics. L\'evy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving…