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Seleznjev, Oleg
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Publications (10 of 30) Show all publications
Hashorva, E., Seleznjev, O. & Tan, Z. (2018). Approximation of maximum of Gaussian random fields. Journal of Mathematical Analysis and Applications, 457(1), 841-867
Open this publication in new window or tab >>Approximation of maximum of Gaussian random fields
2018 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 457, no 1, p. 841-867Article in journal (Refereed) Published
Abstract [en]

This contribution is concerned with Gumbel limiting results for supremum M-n = sup(t epsilon[0,Tn])X(n)(t)vertical bar with X (n) ,n epsilon N-2 centered Gaussian random fields with continuous trajectories. We show first the convergence of a related point process to a Poisson point process thereby extending previous results obtained in [8] for Gaussian processes. Furthermore, we derive Gumbel limit results for M-n as n -> infinity and show a second-order approximation for E{M-n(p)}(1/p) for any p >= 1.

Place, publisher, year, edition, pages
Academic Press, 2018
Keywords
maxima, homogeneous Gaussian random fields, non-homogeneous Gaussian random fields, Pickands constant, Piterbarg constant, Gumbel limit theorem
National Category
Mathematical Analysis Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-141394 (URN)10.1016/j.jmaa.2017.08.040 (DOI)000412152100043 ()
Available from: 2017-11-23 Created: 2017-11-23 Last updated: 2018-06-09Bibliographically approved
Sedaghat, M., Wadbro, E., Wilkes, J., Sjöstedt de Luna, S., Seleznjev, O. & Elmroth, E. (2016). DieHard: Reliable Scheduling to Survive Correlated failures in Cloud Data Centers. In: 2016 16th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGrid): . Paper presented at 16th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID), Cartagena, Colombia, May 16-19, 2016. IEEE
Open this publication in new window or tab >>DieHard: Reliable Scheduling to Survive Correlated failures in Cloud Data Centers
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2016 (English)In: 2016 16th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGrid), IEEE, 2016Conference paper, Published paper (Refereed)
Abstract [en]

In large scale data centers, a single fault can lead to correlated failures of several physical machines and the tasks running on them, simultaneously. Such correlated failures can severely damage the reliability of a service or a job running on the failed hardware. This paper models the impact of stochastic and correlated failures on job reliability in a data center. We focus on correlated failures caused by power outages or failures of network components, on jobs running multiple replicas of identical tasks. We present a statistical reliability model and an approximation technique for computing a job’s reliability in the presence of correlated failures. In addition, we address the problem of scheduling a job with reliability constraints.We formulate the scheduling problem as an optimization problem, with the aim being to maintain the desired reliability with the minimum number of extra tasks to resist failures.We present a scheduling algorithm that approximates the minimum number of required tasks and a placement to achieve a desired job reliability. We study the efficiency of our algorithm using an analytical approach and by simulating a cluster with different failure sources and reliabilities. The results show that the algorithm can effectively approximate the minimum number of extra tasks required to achieve the job’s reliability.

Place, publisher, year, edition, pages
IEEE, 2016
Keywords
Cloud computing, Scheduling; Reliability, Fault tolerance, Correlated failures
National Category
Computer Sciences
Research subject
Computer Science
Identifiers
urn:nbn:se:umu:diva-116791 (URN)10.1109/CCGrid.2016.11 (DOI)
Conference
16th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID), Cartagena, Colombia, May 16-19, 2016
Note

Originally published in manuscript form.

Available from: 2016-02-11 Created: 2016-02-11 Last updated: 2019-06-14Bibliographically approved
Källberg, D. & Seleznjev, O. (2016). Estimation of entropy-type integral functionals. Communications in Statistics - Theory and Methods, 45(4), 887-905
Open this publication in new window or tab >>Estimation of entropy-type integral functionals
2016 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 4, p. 887-905Article in journal (Other academic) Published
Abstract [en]

Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and uncertainty characteristics for a random variable (e.g., Renyi entropy). In this paper, we study U-statistic estimators for a class of such functionals. The estimators are based on ε-close vector observations in the corresponding independent and identically distributed samples. We prove asymptotic properties of the estimators (consistency and asymptotic normality) under mild integrability and smoothness conditions for the densities. The results can be applied in diverse problems in mathematical statistics and computer science (e.g., distribution identication problems, approximate matching for random databases, two-sample problems).

Keywords
Divergence estimation, asymptotic normality, U-statistics, inter-point distances, quadratic functional, entropy estimation
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-60993 (URN)10.1080/03610926.2013.853789 (DOI)000370612900005 ()
Available from: 2012-11-06 Created: 2012-11-06 Last updated: 2018-06-08Bibliographically approved
Hashorva, E., Lifshits, M. & Seleznjev, O. (2015). Approximation of a Random Process with Variable Smoothness. In: Hallin, Marc; Mason, David M.; Pfeifer, Dietmar; Steinebach, Josef G. (Ed.), Mathematical Statistics and Limit Theorems: Festschrift in Honour of Paul Deheuvels (pp. 189-208). Springer International Publishing
Open this publication in new window or tab >>Approximation of a Random Process with Variable Smoothness
2015 (English)In: Mathematical Statistics and Limit Theorems: Festschrift in Honour of Paul Deheuvels / [ed] Hallin, Marc; Mason, David M.; Pfeifer, Dietmar; Steinebach, Josef G., Springer International Publishing , 2015, p. 189-208Chapter in book (Other academic)
Abstract [en]

We consider the rate of piecewise constant approximation to a locally stationary process X(t),t∈[0,1] , having a variable smoothness index α(t) . Assuming that α(⋅) attains its unique minimum at zero and satisfies α(t)=α0+btγ+o(tγ) as t→0, we propose a method for construction of observation points (composite dilated design) such that the integrated mean square error ∫10E{(X(t)−Xn(t))2}dt∼Knα0(logn)(α0+1)/γ as n→∞, where a piecewise constant approximation Xn is based on N(n)∼n observations of X . Further, we prove that the suggested approximation rate is optimal, and then show how to find an optimal constant K .

Place, publisher, year, edition, pages
Springer International Publishing, 2015
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-103713 (URN)10.1007/978-3-319-12442-1_11 (DOI)978-3-319-12441-4 (ISBN)
Note

Originally published in manuscript form.

Available from: 2015-05-28 Created: 2015-05-28 Last updated: 2018-06-07Bibliographically approved
Hashorva, E., Mishura, Y. & Seleznjev, O. (2015). Boundary non-crossing probabilities for fractional Brownian motion with trend. Stochastics: An International Journal of Probablitiy and Stochastic Processes, 87(6), 946-965
Open this publication in new window or tab >>Boundary non-crossing probabilities for fractional Brownian motion with trend
2015 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 87, no 6, p. 946-965Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large trend function. As a by-product, we solve a minimization problem related to the norm of the trend function.

Keywords
boundary crossings, Cameron–Martin–Girsanov theorem, reproducing kernel Hilbert space, large deviation principle, Molchan martingale, fractional Brownian motion
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-103712 (URN)10.1080/17442508.2015.1019882 (DOI)000362724700002 ()
Note

Originally published in manuscript form.

Available from: 2015-05-28 Created: 2015-05-28 Last updated: 2018-06-07Bibliographically approved
Kubilius, K., Mishura, Y., Ralchenko, K. & Seleznjev, O. (2015). Consistency of the drift parameter estimator for the discretized fractional Ornstein–Uhlenbeck process with Hurst index H ∈ (0, 12). Electronic Journal of Statistics, 9, 1799-1825
Open this publication in new window or tab >>Consistency of the drift parameter estimator for the discretized fractional Ornstein–Uhlenbeck process with Hurst index H ∈ (0, 12)
2015 (English)In: Electronic Journal of Statistics, ISSN 1935-7524, E-ISSN 1935-7524, Vol. 9, p. 1799-1825Article in journal (Refereed) Published
Abstract [en]

parameter θ and where the noise is modeled as fractional Brownian motionwith Hurst index H ∈ (0, 12 ). The solution corresponds to the fractionalOrnstein–Uhlenbeck process. We construct an estimator, based on discreteobservations in time, of the unknown drift parameter, that is similar in formto the maximum likelihood estimator for the drift parameter in Langevinequation with standard Brownian motion. It is assumed that the intervalbetween observations is n−1, i.e. tends to zero (high-frequency data) andthe number of observations increases to infinity as nm with m > 1. It isproved that for strictly positive θ the estimator is strongly consistent forany m > 1, while for θ ≤ 0 it is consistent when m > 12H .

Keywords
Fractional Brownian motion, fractional Ornstein– Uhlenbeck process, short-range dependence, drift parameter estimator, consistency, strong consistency, discretization, high-frequency data.
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-109182 (URN)10.1214/15-EJS1062 (DOI)000366270900011 ()
Available from: 2015-09-22 Created: 2015-09-22 Last updated: 2018-06-07Bibliographically approved
Abramowicz, K. & Seleznjev, O. (2015). Stratified Monte Carlo quadrature for continuous random fields. Methodology and Computing in Applied Probability, 17(1), 59-72
Open this publication in new window or tab >>Stratified Monte Carlo quadrature for continuous random fields
2015 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 17, no 1, p. 59-72Article in journal (Refereed) Published
Abstract [en]

We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behavior is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the H¨older class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.

Place, publisher, year, edition, pages
New York: Springer Science+Business Media B.V., 2015
Keywords
numerical integration, random field, sampling design, stratified sampling, Monte Carlo methods
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-60994 (URN)10.1007/s11009-013-9347-6 (DOI)000349406400005 ()
Available from: 2012-11-06 Created: 2012-11-06 Last updated: 2018-06-08Bibliographically approved
Mishura, Y., Ral’chenko, K., Seleznjev, O. & Shevchenko, G. (2014). Asymptotic properties of drift parameter estimator based on discrete observations of stochastic differential equation driven by fractional brownian motion. In: Volodymyr Korolyuk, Nikolaos Limnios, Yuliya Mishura, Lyudmyla Sakhno, Georgiy Shevchenko (Ed.), Modern stochastics and applications: (pp. 303-318). Springer
Open this publication in new window or tab >>Asymptotic properties of drift parameter estimator based on discrete observations of stochastic differential equation driven by fractional brownian motion
2014 (English)In: Modern stochastics and applications / [ed] Volodymyr Korolyuk, Nikolaos Limnios, Yuliya Mishura, Lyudmyla Sakhno, Georgiy Shevchenko, Springer, 2014, p. 303-318Chapter in book (Refereed)
Abstract [en]

In this chapter, we consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic differential equations are constructed. It is proved that the estimators converge almost surely to the parameter value, as the observation interval expands and the distance between observations vanishes. A bound for the rate of convergence is given and numerical simulations are presented. As an auxilliary result of independent interest we establish global estimates for fractional derivative of fractional Brownian motion.

Place, publisher, year, edition, pages
Springer, 2014
Series
Springer optimization and its applications, ISSN 1931-6828 ; 90
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-81372 (URN)10.1007/978-3-319-03512-3_17 (DOI)978-3-319-03511-6 (ISBN)978-3-319-03512-3 (ISBN)
Available from: 2013-10-08 Created: 2013-10-08 Last updated: 2018-06-08Bibliographically approved
Ali-Eldin, A., Rezaie, A., Mehta, A., Razroev, S., Sjöstedt-de Luna, S., Seleznjev, O., . . . Elmroth, E. (2014). How will your workload look like in 6 years?: Analyzing Wikimedia's workload. In: Lisa O’Conner (Ed.), Proceedings of the 2014 IEEE International Conference on Cloud Engineering (IC2E 2014): . Paper presented at IC2E 2014, IEEE International Conference on Cloud Engineering, Boston, Massachusetts, 11-14 March 2014 (pp. 349-354). IEEE Computer Society
Open this publication in new window or tab >>How will your workload look like in 6 years?: Analyzing Wikimedia's workload
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2014 (English)In: Proceedings of the 2014 IEEE International Conference on Cloud Engineering (IC2E 2014) / [ed] Lisa O’Conner, IEEE Computer Society, 2014, p. 349-354Conference paper, Published paper (Refereed)
Abstract [en]

Accurate understanding of workloads is key to efficient cloud resource management as well as to the design of large-scale applications. We analyze and model the workload of Wikipedia, one of the world's largest web sites. With descriptive statistics, time-series analysis, and polynomial splines, we study the trend and seasonality of the workload, its evolution over the years, and also investigate patterns in page popularity. Our results indicate that the workload is highly predictable with a strong seasonality. Our short term prediction algorithm is able to predict the workload with a Mean Absolute Percentage Error of around 2%.

Place, publisher, year, edition, pages
IEEE Computer Society, 2014
Series
IEEE, ISSN 2373-3845
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Computer Systems
Research subject
Computing Science
Identifiers
urn:nbn:se:umu:diva-87235 (URN)10.1109/IC2E.2014.50 (DOI)000361018600043 ()978-1-4799-3766-0 (ISBN)
Conference
IC2E 2014, IEEE International Conference on Cloud Engineering, Boston, Massachusetts, 11-14 March 2014
Funder
Swedish Research Council, C0590801eSSENCE - An eScience Collaboration
Available from: 2014-03-25 Created: 2014-03-25 Last updated: 2018-06-08Bibliographically approved
Ali-Eldin, A., Seleznjev, O., Sjöstedt-de Luna, S., Tordsson, J. & Elmroth, E. (2014). Measuring cloud workload burstiness. In: 2014 IEEE/ACM 7th International Conference on Utility and Cloud Computing (UCC): . Paper presented at 7th International Conference on Utility and Cloud Computing (UCC), 8-11 December 2014, London, England, United Kingdom (pp. 566-572). IEEE conference proceedings
Open this publication in new window or tab >>Measuring cloud workload burstiness
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2014 (English)In: 2014 IEEE/ACM 7th International Conference on Utility and Cloud Computing (UCC), IEEE conference proceedings, 2014, p. 566-572Conference paper, Published paper (Refereed)
Abstract [en]

Workload burstiness and spikes are among the main reasons for service disruptions and decrease in the Quality-of-Service (QoS) of online services. They are hurdles that complicate autonomic resource management of datacenters. In this paper, we review the state-of-the-art in online identification of workload spikes and quantifying burstiness. The applicability of some of the proposed techniques is examined for Cloud systems where various workloads are co-hosted on the same platform. We discuss Sample Entropy (SampEn), a measure used in biomedical signal analysis, as a potential measure for burstiness. A modification to the original measure is introduced to make it more suitable for Cloud workloads.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2014
National Category
Computer Systems
Identifiers
urn:nbn:se:umu:diva-108397 (URN)10.1109/UCC.2014.87 (DOI)000380558700080 ()978-1-4799-7881-6 (ISBN)
Conference
7th International Conference on Utility and Cloud Computing (UCC), 8-11 December 2014, London, England, United Kingdom
Funder
EU, European Research CouncilSwedish Research Council
Available from: 2015-09-10 Created: 2015-09-10 Last updated: 2018-06-07Bibliographically approved
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