Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.

-The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for a stochastic system driven by discontinuous (with jumps) Lévy motion. This paper discusses the two deterministic quantities, mean first exit time and escape probability, for the anomalous processes having the tempered Lévy stable waiting times with the tempering index µ > 0 and the stability index 0 < α ≤ 1; as for the distribution of jump lengths (in the CTRW framework) or the type of the noises driving the system (in the Langevin picture), two cases are considered, i.e., Gaussian white noise and non-Gaussian (tempered) β-stable (0 < β < 2) Lévy noise. Firstly, we derive the nonlocal elliptic partial differential equations (PDEs) governing the mean first exit time and escape probability. Based on the derived PDEs, it is observed that the mean first exit time depends strongly on the domain size and the values of α, β and µ; when µ is close to zero, the mean first exit time tends to ∞. In particular, we also find an interesting result that the escape probability of a particle with (tempered) power-law jumping length distribution has no relation with the distribution of waiting times for the model considered in this paper. For the solutions of the derived PDEs, the boundary layer phenomena are observed, which inspires the motivation for developing the boundary layer theory for nonlocal PDEs.Introduction. -Anomalous diffusion phenomena are widely found in natural world; the subdiffusion includes, e.g., motion of lipids on membranes, solute transport in porous media, translocation of polymers; and the superdiffuion is observed in, e.g., turbulent flow, optical materials, motion of predators, human travel, etc [1]. The types of diffusion are usually distinguished by the exponent of the evolution of the second order moment of a stochastic process x(t) with respect to the time t, i.e., x T (t)x(t) ∼ t γ ; when γ = 1, it is normal diffusion; γ < 1 corresponds to subdiffusion and γ > 1 superdiffusion.

No abstract

Strongly intensive quantities Σ[P T , N] and Δ[P T , N] have become one of the important tools in study of phase transitions and critical points in high energy heavy-ion collisions. In this paper the properties of Σ[P T , N] and Δ[P T , N] are discussed within different colliding nuclei systems generated by the AMPT model. The combined event method are proposed to simulate the model of independent sources in which Σ[P T , N] and Δ[P T , N] are independent of the number of original events. The effects of transverse momentum, pseudorapidity and parton cascade are also discussed.

No abstract