Change-point detection for Lévy processes

Figueroa-López, José E.; Ólafsson, Sveinn

doi:10.1214/17-aap1368

Cited by 5 publications

(3 citation statements)

References 22 publications

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“…where we recall that E 2 τ ,δ, CU SU M is the worst mean delay defined in (7). Equation (9) states that…”

Section: Intermediary Resultsmentioning

confidence: 99%

“…They used the classical CUSUM rule to determine the change time. As for [9], they considered the change detection problem for continuous-time Lévy processes by approximating an adapted sequence of change-point problems and where the optimality of a CUSUM rule is shown. To sum up, in the previous works, the proposed techniques were based on an a priori distribution for the change-time or a deterministic unknown change-time.…”

Section: Introductionmentioning

confidence: 99%

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Change-level detection for Lévy subordinators

Masry

Verdier

2022

Stochastic Processes and their Applications

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Let X = (X t ) t≥0 be a process behaving as a general increasing Lévy process (subordinator) prior to hitting a given unknown level m 0 , then behaving as another different subordinator once this threshold is crossed. This paper addresses the detection of this unknown threshold m 0 ∈ [0, +∞] from an observed trajectory of the process. These kind of model and issue are encountered in many areas such as reliability and quality control in degradation problems. More precisely, we construct, from a sample path and for each > 0, a so-called detection level L by considering a CUSUM inspired procedure. Under mild assumptions, this level is such that, while m 0 is infinite (i.e. when no changes occur), its expectation E ∞ (L ) tends to +∞ as tends to 0, and the expected overshoot E m0 ([L − m 0 ] + ), while the threshold m 0 is finite, is negligible compared to E ∞ (L ) as tends to 0. Numerical illustrations are provided when the Lévy processes are gamma processes with different shape parameters.

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“…where we recall that E 2 τ ,δ, CU SU M is the worst mean delay defined in (7). Equation (9) states that…”

Section: Intermediary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Change-level detection for Lévy subordinators

Masry

Verdier

2022

Stochastic Processes and their Applications

View full text Add to dashboard Cite

show abstract

“…The paper [20] studies this in detail, with the goal of change detection through discrimination among an arbitrary number of hypotheses by analyzing the likelihood of each hypothesis. Another ( [24]) studies the problem through the analysis of equispaced sampling points approximating the continuous-time Lévy processes. Problems like these are of particular interest in finance, as seen by commonly used "close" and "open" prices of stocks and commodities.…”

Section: Introductionmentioning

confidence: 99%

Hypothesis tests on high dimensional datastreams, with finance application

Roberts,

Cao,

Awasthi

2024

Preprint

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In this paper, we present the testing of many hypotheses on multiple streams of observations that are driven by Lévy processes. This is applicable for sequential decisionmaking on the state of multi-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data driven by Lévy processes with large or small jumps. In either case, these give rise to 2n possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.

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Multivariate Lévy-type drift change detection and mortality modeling

Krawiec

Palmowski

2023

Eur. Actuar. J.

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In this paper we give a solution to the quickest drift change detection problem for a multivariate Lévy process consisting of both continuous (Gaussian) and jump components in the Bayesian approach. We do it for a general 0-modified continuous prior distribution of the change point as well as for a random post-change drift parameter. Classically, our criterion of optimality is based on a probability of false alarm and an expected delay of the detection, which is then reformulated in terms of a posterior probability of the change point. We find a generator of the posterior probability, which in case of general prior distribution is inhomogeneous in time. The main solving technique uses the optimal stopping theory and is based on solving a certain free-boundary problem. We also construct a Generelized Shiryaev-Roberts statistic, which can be used for applications. The paper is supplemented by two examples, one of which is further used to analyze Polish life tables (after proper calibration) and detect the drift change in the correlated force of mortality of men and women jointly.

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Change-point detection for Lévy processes

Cited by 5 publications

References 22 publications

Change-level detection for Lévy subordinators

Change-level detection for Lévy subordinators

Hypothesis tests on high dimensional datastreams, with finance application

Multivariate Lévy-type drift change detection and mortality modeling

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