?
Statistical inference for time-changed Lévy processes via Mellin transform approach
Stochastic Processes and their Applications. 2016. Vol. 126. No. 7. P. 2092–2122.
Belomestny D., Schoenmakers J.
Given a Lévy process (Lt)t≥0 and an independent nondecreasing process (time change) (T(t))t≥0, we consider the problem of statistical inference on T based on low-frequency observations of the time-changed Lévy process LT(t). Our approach is based on the genuine use of Mellin and Laplace transforms. We propose a consistent estimator for the density of the increments of T in a stationary regime, derive its convergence rates and prove the optimality of the rates. It turns out that the convergence rates heavily depend on the decay of the Mellin transform of T. Finally, the performance of the estimator is analysed via a Monte Carlo simulation study.
Belomestny D., Morozova E., Panov V., Statistics 2024 Vol. 58 No. 4 P. 943–960
This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables \(\xi_1+...+\xi_N\), where the number of summands, \(N\), is a random variable independent of \(\xi_1, \xi_2,...\) Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for ...
Added: August 21, 2024
Manita A., , in: Analytical and Computational Methods in Probability TheoryVol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin: Springer, 2017. P. 347–360.
We consider Markov models of multicomponent systems with synchronizing interaction. Under natural regularity assumptions about the message routing graph, they have nice longtime behavior. We are interested in limit probability laws related to the steady state viewed from the center-of-mass coordinate system. ...
Added: July 16, 2018
Grishunina Y., Manita L., , in: Analytical and Computational Methods in Probability TheoryVol. 10684: Analytical and Computational Methods in Probability Theory.: Berlin: Springer, 2017. P. 75–82.
We construct a mathematical model of anti-virus protection of local area networks. The model belongs to the class of regenerative processes. To protect the network from the external attacks of viruses and the spread of viruses within the network we apply two methods: updating antivirus signatures and reinstallings of operating systems (OS). Operating systems are ...
Added: July 2, 2018
Yu. Grishunina, L. Manita, , in: Analytical and computational methods in probability theory and its applications (ACMPT-2017). Proceedings of the International Scientific Conference.: M.: RUDN, 2017. P. 80–84.
We construct a mathematical model of anti-virus protection of local area networks. The
model belongs to the class of regenerative processes. To protect the network from the
external attacks of viruses and the spread of viruses within the network we apply two
methods: updating antivirus signatures and reinstallings of operating systems (OS).
Operating systems are reinstalled in the case ...
Added: June 20, 2018
Panov V., Samarin E., / Series arXiv "math". 2018. No. 1802.02876.
Added: February 9, 2018
Belomestny D., Panov V., Statistics 2018 Vol. 52 No. 3 P. 571–589
In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers nonparametrically the density of ...
Added: January 19, 2018
Grishunina Y., Manita L., Lecture Notes in Computer Science 2017 Vol. 10684 P. 75–82
We construct a mathematical model of anti-virus protection of local area networks. The model belongs to the class of regenerative processes. To protect the network from the external attacks of viruses and the spread of viruses within the network we apply two methods: updating antivirus signatures and reinstallings of operating systems (OS). Operating systems are ...
Added: December 22, 2017
Belomestny D., Panov V., Woerner J., Bernoulli: a journal of mathematical statistics and probability 2019 Vol. 25 No. 2 P. 902–931
In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form
\[ Z_{t}=\int_{\R}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}, \] with a deterministic kernel \(\K\) and a L{\'e}vy process \(L\). Especially the estimation of the L\'evy measure \(\nu\) of $L$ from low-frequency observations of the process $Z$ is considered. We construct ...
Added: December 9, 2017
Belomestny D., Mai H., Schoenmakers J., Journal of Mathematical Analysis and Applications 2017 No. 455 P. 89–104
In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post– Widder formula. We establish convergence of our inversion method and derive the corresponding convergence rates for the case of a Laplace transform of a smooth density. ...
Added: September 22, 2017
Belomestny D., Panov V., / Series ArXiv.org "Stat". 2017. No. 1705.07578.
In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers nonparametrically the density of ...
Added: May 23, 2017
Belomestny D., Panov V., Woerner J., / Series arXiv "math". 2016. No. 1607.00896.
In this paper we study the problem of statistical inference for a continuous time moving average L\'evy process \(Z\) observed at low-frequency. We construct a consistent estimator for the L\'evy triplet of \(Z\), derive its convergence rates and prove their optimality. The performance of our estimation procedure is illustrated by numerical example. ...
Added: July 5, 2016
Pospelov I. G., Radionov S., / Series arXiv "math". 2015. No. 1509.06945.
We study the asymmetric one-dimensional telegraph process in the bounded domain. Lower boundary is absorbing and upper boundary is reflecting with delay. Point stays in the upper boundary until switch of regime occurs. We obtain the distribution of this process in terms of Laplace trasforms ...
Added: October 22, 2015
Belomestny D., Panov V., Electronic journal of statistics 2015 Vol. 9 No. 2 P. 1974–2006
In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type
\[
X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right),
\]
where \(\xi_s\) is a L{\'e}vy process. Our primal goal is to estimate the characteristics of the L\'evy process \(\xi\) from the low-frequency observations of the process \(X\). We present ...
Added: September 1, 2015
Panov V., Methodology and Computing in Applied Probability 2017 Vol. 19 No. 1 P. 97–119
In this paper, we analyze a L{\'e}vy model based on two popular concepts - subordination and L{\'e}vy copulas. More precisely, we consider a two-dimensional L{\'e}vy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between subordinators is described via some L{\'e}vy copula. The main result of this paper is the ...
Added: August 31, 2015
Belomestny D., Schoenmakers J., Statistics and Probability Letters 2015 Vol. 104 P. 169–180
Given a Brownian motion B, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time T based on i.i.d. sample from BT. We propose a consistent estimator for the density of T, derive its convergence rates and prove their optimality. ...
Added: July 28, 2015
Panov V., Sirotkin I., / Series math "arxiv.org". 2015. No. 1503.02214.
In this paper, we analyze a L{\'e}vy model based on two popular concepts - subordination and L{\'e}vy copulas. More precisely, we consider a two-dimensional L{\'e}vy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between processes, which are used for stochastic time change, is described via some L{\'e}vy copula. We ...
Added: March 10, 2015