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Title: | A study of Component-Wise Semi-Markov Process |
Authors: | GOSWAMI, ANINDYA YADAV, RAVISHANKAR KAPILDEV Dept. of Mathematics 20173545 |
Keywords: | Mathematics Stochastic Differential Equation semi-Markov Process Component-wise semi-Markov Process Meeting and merging coupling |
Issue Date: | Apr-2023 |
Citation: | 117 |
Abstract: | Component-wise semi-Markov processes (CSM) constitute a larger class of pure jump processes which includes semi-Markov, and Markov pure jump processes. This thesis examines semi-Markov as well as CSM processes with dependent components. In order to better understand the interactions among components of CSM processes having bounded transition rates, we consider a family of stochastic flows using a system of SDEs driven by Poisson random measure (PRM), with an additional gaping parameter. More specifically, we have demonstrated that the proposed system of SDEs driven by a PRM does, in fact, has a unique solution. Then, we prove that a solution satisfies the desired law. Thus we establish a semimartingale representation of the homogeneous or nonhomogeneous semi-Markv process. Finally, we pick up an appropriate flow by fixing the gaping parameter. We derive expressions of the probabilities of meeting and merging of a pair of semi-Markov processes, solving the same equation but with different initial conditions. We also obtain a set of sufficient |
URI: | http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7801 |
Appears in Collections: | PhD THESES |
Files in This Item:
File | Description | Size | Format | |
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20173545_Ravi_Yadav_PhD_Thesis.pdf | PhD Thesis | 1.25 MB | Adobe PDF | View/Open |
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