Related papers: Levy flights in a box
We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in…
We study L\'evy flights confined in a parabolic potential. This has to do with a fractional generalization of ordinary quantum-mechanical oscillator problem. To solve the spectral problem for the fractional quantum oscillator, we pass to…
An impact of integration over the paths of the Levy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox H-function. A new equation for the kernel…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…
We investigate the non-Langevin relative of the L\'{e}vy-driven Langevin random system, under an assumption that both systems share a common (asymptotic, stationary, steady-state) target pdf. The relaxation to equilibrium in the fractional…
Rough path analysis can be developed using the concept of controlled paths, and with respect to a topology in which L\'evy's area plays a role. For vectors of irregular paths we investigate the relationship between the property of being…
We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger…
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
L\'evy flights and L\'evy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities are discontinuity versus continuity of their trajectories and…
L\'{e}vy flights can be described using a Fokker-Planck equation which involves a fractional derivative operator in the position co-ordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show…
We study symmetric L\'evy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the L\'evy process. Incorporating the boundary…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
We study the quantum walk subjected to measurements with a L\'evy waiting-time distribution. We find that the system has a sub-ballistic behavior instead of a diffusive one. We obtain an analytical expression for the exponent of the power…
Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of a particle trapping in a…
We provide a L\'evy-It\^o decomposition of sample paths of L\'evy processes with values in complete locally convex Suslin spaces. This class of state spaces contains the well investigated examples of separable Banach spaces, as well as…
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the…
We give a modified Hamiltonian for a particle in a box with infinite potential walls that takes into account wall effects. The Hamiltonian is expressed in both the position and momentum representation. In the momentum representation the…