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Jevgenijs Ivanovs – One of the best experts on this subject based on the ideXlab platform.
Splitting and time reversal for Markov Additive ProcessesStochastic Processes and their Applications, 2017Co-Authors: Jevgenijs IvanovsAbstract:
We consider a Markov Additive Process with a finite phase space and study its path decompositions at the times of extrema, first passage and last exit. For these three families of times we establish splitting conditional on the phase, and provide various relations between the laws of post- and pre-splitting Processes using time reversal. These results offer valuable insight into the behaviour of the Process, and while being structurally similar to the Levy Process case, they demonstrate various new features. As an application we formulate the Wiener–Hopf factorization, where time is counted in each phase separately and killing of the Process is phase dependent. Restricting to the case of no positive jumps, we find concise formulas for these factors, and also characterize the time of last exit from the negative half-line. The latter result is obtained using three quite different approaches based on the established path decomposition theory, which further demonstrates its applicability.
Splitting and time reversal for Markov Additive ProcessesarXiv: Probability, 2015Co-Authors: Jevgenijs IvanovsAbstract:
We consider a Markov Additive Process with a finite phase space and study its path decompositions at the times of extrema, first passage and last exit. For these three families of times we establish splitting conditional on the phase, and provide various relations between the laws of post- and pre-splitting Processes using time reversal. These results offer valuable insight into behavior of the Process, and while being structurally similar to the L\’evy Process case, they demonstrate various new features. As an application we formulate the Wiener-Hopf factorization, where time is counted in each phase separately and killing of the Process is phase dependent. Assuming no positive jumps, we find concise formulas for these factors, and also characterize the time of last exit from the negative half-line using three different approaches, which further demonstrates applicability of path decomposition theory.
Potential measures of one-sided Markov Additive Processes with reflecting and terminating barriersJournal of Applied Probability, 2014Co-Authors: Jevgenijs IvanovsAbstract:
Consider a one-sided Markov Additive Process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and nondefective Processes, and all possible scenarios, we identify the corresponding potential measures, which help to generalize a number of results for one-sided Levy Processes. The resulting rather neat formulae have various applications in risk and queueing theories, and, in particular, they lead to quasistationary distributions of the corresponding Processes.
Mrh Michel Mandjes – One of the best experts on this subject based on the ideXlab platform.
first passage of a markov Additive Process and generalized jordan chainsJournal of Applied Probability, 2010Co-Authors: Bernardo Dauria, Jevgenijs Ivanovs, Offer Kella, Mrh Michel MandjesAbstract:
In this paper we consider the first passage Process of a spectrally negative Markov Additive Process (MAP). The law of this Process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of Jordan chains associated with analytic matrix functions. This result provides us with a technique, which can be used to derive various further identities.
Singularities of the matrix exponent of a Markov Additive Process with one-sided jumpsStochastic Processes and their Applications, 2010Co-Authors: Jevgenijs Ivanovs, Onno Boxma, Mrh Michel MandjesAbstract:
We analyze the number of zeros of det(F([alpha])), where F([alpha]) is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps. The focus is on the number of zeros in the right half of the complex plane, where F([alpha]) is analytic. In addition, we also consider the case of a MAP killed at an independent exponential time. The corresponding zeros can be seen as the roots of a generalized Cramer-Lundberg equation. We argue that our results are particularly useful in fluctuation theory for MAPs, which leads to numerous applications in queueing theory and finance.
On the record Process of time-reversible spectrally-negative Markov Additive Processes, 2009Co-Authors: Jevgenijs Ivanovs, Mrh Michel MandjesAbstract:
We study the record Process of a spectrally-negative Markov Additive Process (MAP). Assuming time-reversibility, a number of key quantities can be given explicitly. It is shown how these key quantities can be used when analyzing the distribution of the all-time maximum attained by MAPs with negative drift, or, equivalently, the stationary workload distribution of the associated storage system; the focus is on Markov-modulated Brownian mo- tion, spectrally-negative and spectrally-positive MAPs. It is also argued how our results are of great help in the numerical analysis of systems in which the driving MAP is a superposition of multiple time-reversible MAPs.
Jean-yves Hascoet – One of the best experts on this subject based on the ideXlab platform.
A new DFM approach to combine machining and Additive manufacturingComputers in Industry, 2011Co-Authors: Olivier Kerbrat, Pascal Mognol, Jean-yves HascoetAbstract:
Design For Manufacturing (DFM) approaches aim to integrate manufacturability aspects during the design stage. Most of DFM approaches usually consider only one manufacturing Process, but products competitiveness may be improved by designing hybrid modular products, in which products are seen as 3-D puzzles with modules realized aside by the best manufacturing Process and further gathered. A new DFM system is created in order to give quantitative information during the product design stage of which modules will benefit in being machined and which ones will advantageously be realized by an Additive Process (such as Selective Laser Sintering or laser deposition). A methodology for a manufacturability evaluation in case of a subtractive or an Additive manufacturing Process is developed and implemented in a CAD software. Tests are carried out on industrial products from automotive industry.
Manufacturing complexity evaluation at the design stage for both machining and layered manufacturingCIRP Journal of Manufacturing Science and Technology, 2010Co-Authors: Olivier Kerbrat, Pascal Mognol, Jean-yves HascoetAbstract:
In this paper, a methodology to estimate manufacturing complexity for both machining and layered manufacturing is proposed in order to realize tools (dies or molds) by a combination of a subtractive and an Additive Process. Manufacturability indexes are calculated at the tool design stage, these indexes provide an accurate view of which areas of the tool will advantageously be machined or manufactured by an Additive Process. In this case, tools are not seen as single pieces but as 3-D puzzles with modules, manufactured aside by the best Process and further assembled.
Manufacturability analysis to combine Additive and subtractive ProcessesRapid Prototyping Journal, 2010Co-Authors: Olivier Kerbrat, Pascal Mognol, Jean-yves HascoetAbstract:
Purpose – The purpose of this paper is to propose a methodology to estimate manufacturing complexity for both machining and layered manufacturing. The goal is to take into account manufacturing constraints at design stage in order to realize tools (dies and molds) by a combination of a subtractive Process (high‐speed machining) and an Additive Process (selective laser sintering).Design/methodology/approach – Manufacturability indexes are defined and calculated from the tool computer‐aided design (CAD) model, according to geometric, material and specification information. The indexes are divided into two categories: global and local. For local indexes, a decomposition of the tool CAD model is used, based on an octree decomposition algorithm and a map of manufacturing complexity is obtained.Findings – The manufacturability indexes values provide a well‐detailed view of which areas of the tool may advantageously be machined or manufactured by an Additive Process.Originality/value – Nowadays, layered manufact…