Related papers: The Langevin function and truncated exponential di…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…
A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from…
A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words of length N from an alphabet of k letters. We find Toeplitz determinant representations for the exponential…
In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as…
We provide sharp estimates for the distribution function of a martingale transform of the indicator function of an event. They are formulated in terms of Burkholder functions, which are reduced to the already known Bellman functions for…
This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optimal variance proxy as the unique solution to a set of two…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections)…
We analyse a random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, hence plays an…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient…