Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7801
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
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