Related papers: The Langevin function and truncated exponential di…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the…
For a difference approximations of multidimensional diffusion, the truncated local limit theorem is proved. Under very mild conditions on the distribution of the difference terms, this theorem provides that the transition probabilities of…
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto…
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…
In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical…
Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion…
An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding…
The statistical parameters of five generalizations of the Lindley distribution, such as the average, variance and moments, are reviewed. A new double truncated Lindley distribution with three parameters is derived. The new distributions are…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Consider the well-known Langevin diffusion on $\mathbb{R}^d$ $$\mathrm{d} X_t = -\nabla U(X_t)\,\mathrm{d} t + \sqrt{2}\mathrm{d} B_t, $$ and its Euler-Maruyama discretization given by $$X_{k+1}=X_k-\eta \nabla U(X_k)+\sqrt{2\eta…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…
The inverse Langevin function is a fundamental part of the statistical chain models used to describe the behavior of polymeric-like materials, appearing also in other fields such as magnetism, molecular dynamics and even biomechanics. In…
The Laguerre functions $l_{n,\tau}^\alpha$, $n=0,1,\dots$, are constructed from generalized Laguerre polynomials. The functions $l_{n,\tau}^\alpha$ depend on two parameters: scale $\tau>0$ and order of generalization $\alpha>-1$, and form…
This article aims to introduced a new lifetime distribution named as exponentiated xgamma distribution (EXGD). The new generalization obtained from xgamma distribution, a special finite mixture of exponential and gamma distributions. The…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…