arXiv subjects

Alexander Kreinin

Publications and source records attributed to Alexander Kreinin.

5 recordsLinked to original sources

arXiv2025

On generalized Lambert function

We consider a particular generalized Lambert function, $y(x)$, defined by the implicit equation $y^β= 1 - e^{-xy}$, with $x>0$ and $ β> 1$. Solutions to this equation can be found in terms of a certain continued exponential. Asymptotic and structural properties of a non-trivial solution, $y_β(x)$, and its connection to the extinction probability of related branching processes are discussed. We demonstrate that this function constitutes a cumulative distribution function of a previously unknown non-negative absolutely continuous random variable.

math.GM↗

arXiv2021

Backward Simulation of Multivariate Mixed Poisson Processes

The simulation of correlated multivariate Poisson processes with negative correlation between their components has many important applications in Finance, Insurance, Geophysics, and many other areas of applied probability. Introduced in our earlier work, the Backward Simulation (BS) approach to the simulation of correlated multivariate Poisson processes is able to capture a wide range of correlation, including extreme positive and extreme negative correlation, that is not possible with other approaches such as the forward simulation approach. Moreover, the BS approach enables simple and efficient generation of sample paths of correlated multivariate Poisson processes. In this work, we extend the BS approach to multivariate mixed Poisson processes.

stat.CO↗

arXiv2017

Correlated Multivariate Poisson Processes and Extreme Measures

Multivariate Poisson processes have many important applications in Insurance, Finance, and many other areas of Applied Probability. In this paper we study the backward simulation approach to modelling multivariate Poisson processes and analyze the connection to the extreme measures describing the joint distribution of the processes at the terminal simulation time.

stat.ME↗

arXiv2014

Combinatorial Properties of Mills Ratio

We consider combinatorial properties of the Mills' ratio, and explore the interplay between a continued fraction expansion for the Mills' ratio, the Laplace polynomials and a new family of combinatorial identities.

math.CO↗

arXiv2011

The Generalized Shiryaev's Problem and Skorohod Embedding

In this paper we consider a connection between the famous Skorohod embedding problem and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion: given a probability distribution, $F$, find a boundary such that the first hitting time distribution is $F$. By randomizing the initial state of the process we show that the inverse problem becomes analytically tractable. The randomization of the initial state allows us to significantly extend the class of target distributions in the case of a linear boundary and moreover allows us to establish connection with the Skorohod embedding problem.

math.PR↗