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Titlebook: Discrete-Time Semi-Markov Random Evolutions and Their Applications; Nikolaos Limnios,Anatoliy Swishchuk Book 2023 The Editor(s) (if applic

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Franz Glombitza,Rene Kermer,Susan ReichelThis chapter presents the useful material needed in the sequel, in particular, elements of the martingales and martingale problem in Banach space, weak convergence in Banach space, Markov processes, semigroup theory, semi-Markov processes, reducible-invertible operators, and singular perturbed operators.
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Economic Aspects of Industrial BiotechnologyThis chapter presents the basic theory of general state space semi-Markov chains, as well as the splitting and merging of their phase space. New results in discrete-time are also presented, such as the compensating operator, stationary phase merging, and semimartingale decomposition.
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A Brief Survey of the Literature,This chapter presents an optimal stopping problem for geometric Markov renewal chains and pricing in financial mathematics for American and European options. The martingale properties of the discount price and optimal stopping rules are derived. All results are proven in detail.
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Discrete-Time Stochastic Calculus in Banach Space,This chapter presents the useful material needed in the sequel, in particular, elements of the martingales and martingale problem in Banach space, weak convergence in Banach space, Markov processes, semigroup theory, semi-Markov processes, reducible-invertible operators, and singular perturbed operators.
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https://doi.org/10.1007/978-3-031-33429-0Random Evolutions; Semi-Markov Chains; Discrete-Time Semi-Markov Chains; Discrete-Time Random Evolution
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978-3-031-33431-3The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Discrete-Time Semi-Markov Random Evolutions and Their Applications978-3-031-33429-0Series ISSN 2297-0371 Series E-ISSN 2297-0398
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https://doi.org/10.1007/978-3-030-47066-1mes, and tightness of probability measures. The stochastic systems that are considered in the sequel are also presented and formulated in terms of random evolution as additive functionals, geometric Markov renewal chains, and dynamical systems. The general series scheme is presented.
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