相关论文: On Distributions of Certain State Dependent Fracti…

We study the two-dimensional joint distribution of the first hitting time of a constant level by a continuous-state branching process with immigration and their primitive stopped at this time. We show an explicit expression of its Laplace…

In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where…

We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local…

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…

This paper presents a novel method that allows to generalise the use of the Adam-Bashforth to Partial Differential Equations with local and non local operator. The Method derives a two step Adam-Bashforth numerical scheme in Laplace space…

We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…

We consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak…

This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…

In this paper, we obtain some additional probabilistic properties of the renewal process $\{\hat{N}_{\alpha}(t)\}_{t\ge0}$, $0<\alpha\le 1$ introduced by Beghin and Orsingher (2010). A time-changed relationship connecting…

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…

We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…

This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to…

Analytical and numerical techniques have been developed for solving fractional partial differential equations (FPDEs) and their systems with initial conditions. However, it is much more challenging to develop analytical or numerical…

In this paper we study explicit strong solutions for two difference-differential fractional equations, defined via the generator of an immigration-death process, by using spectral methods. Moreover, we give a stochastic representation of…

We consider the change-point problem for the marginal distribution of subordinated Gaussian processes that exhibit long-range dependence. The asymptotic distributions of Kolmogorov-Smirnov- and Cram\'{e}r-von Mises type statistics are…

Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…

The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the…

A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the…

A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…