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ویرایش: [1st ed. 2022]
نویسندگان: Dmitrii Silvestrov
سری:
ISBN (شابک) : 3030924025, 9783030924027
ناشر: Springer
سال نشر: 2022
تعداد صفحات: 418
[406]
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 3 Mb
در صورت تبدیل فایل کتاب Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب فرآیندهای نوع نیمه مارکوف آشفته I: قضایای حدی برای زمان ها و فرآیندهای رویداد نادر نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
Preface Contents List of symbols 1 Introduction 1.1 Part I: First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes 1.1.1 Part I: Contents, Examples, Models, Results 1.1.2 Part I: Contents by Chapters 1.2 Part II: Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes 1.2.1 Part II: Contents, Examples, Models, Results 1.2.2 Part II: Contents by Chapters 1.3 Appendices and Conclusion 1.3.1 Appendix A: Limit Theorems for Randomly Stopped Stochastic Processes 1.3.2 Appendix B: Methodological and Bibliographical Notes 1.3.3 Conclusion Part I First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes 2 Asymptotics of First-Rare-Event Times for Regularly Perturbed Semi-Markov Processes 2.1 First-Rare-Event Times for Perturbed Semi-Markov Processes 2.1.1 First-Rare-Event Times 2.1.2 Asymptotically Uniformly Ergodic Markov Chains 2.1.3 Necessary and Sufficient Conditions for Convergence in Distribution of First-Rare-Event Times 2.2 Asymptotics of Step-Sum Reward Processes 2.2.1 Necessary and Sufficient Conditions for Convergence in Distribution for Step-Sum Reward Processes 2.2.2 Examples of Step-Sum Reward Processes 2.3 Asymptotics of First-Rare-Event Times for Perturbed Markov Chains 2.3.1 Convergence in Distribution for First-Rare-Event Times for Perturbed Markov Chains 2.3.2 J-Convergence for First-Rare-Event Time Processes for Perturbed Markov Chains 2.4 Asymptotics of First-Rare-Event Times for Perturbed Semi-Markov Processes 2.4.1 Convergence in Distribution for First-Rare-Event Times for Perturbed Semi-Markov Processes 2.4.2 J-Convergence for First-Rare-Event Processes for Perturbed Semi-Markov Process 3 Flows of Rare Events for Regularly Perturbed Semi-Markov Processes 3.1 Counting Processes Generated by Flows of Rare Events 3.1.1 Counting Processes for Rare Events 3.1.2 Necessary and Sufficient Conditions of Convergence for Counting Processes Generated by Flows of Rare Events 3.2 Markov Renewal Processes Generated by Flows of Rare Events 3.2.1 Return Times and Rare Events 3.2.2 Necessary and Sufficient Conditions of Convergence for Markov Renewal Processes Generated by Flows of Rare Events 3.3 Vector Counting Processes Generated by Flows of Rare Events 3.3.1 Vector Counting Processes for Rare Events 3.3.2 Necessary and Sufficient Conditions of Convergence for Vector Counting Process Generated by Flows of Rare Events 4 Generalisations of Limit Theorems for First-Rare-Event Times 4.1 Modifications of First-Rare-Event Times and Rare-Event Time Processes 4.1.1 Vector First-Rare-Event Times and Rewards 4.1.2 Upper and Lower First-Rare-Event Times 4.1.3 First-Rare-Event Times for Markov Renewal Processes with Transition Periods 4.1.4 First-Rare-Event Times for Markov Renewal Processes with Extending Phase Spaces 4.2 First-Rare-Event Times and Hitting Times 4.2.1 Necessary and Sufficient Conditions of Convergence in Distribution for Standard Hitting Times 4.2.2 Necessary and Sufficient Conditions of Convergence in Distribution for Directed Hitting Times 5 First-Rare-Event Times for Perturbed Risk Processes 5.1 Stable Asymptotics of First-Rare-Event Times 5.2 Necessary and Sufficient Conditions for Stable Approximation of Non-ruin Distribution Functions 6 First-Rare-Event Times for Perturbed Closed Queuing Systems 6.1 Queuing Systems with Rare Events Caused by Too Long Service Times 6.1.1 Asymptotic Uniform Ergodicity for Birth–Death Markov Chains 6.1.2 M/M-Type Queuing System with Rare Events Caused by Too Long Service Times 6.2 Queuing Systems with Highly Reliable Servers 7 First-Rare-Event Times for Perturbed M/M-Type Queuing Systems 7.1 Rare Events for Queuing Systems with Bounded Buffers 7.1.1 Queuing Systems with a Buffer of Fixed Size 7.1.2 Queuing Systems with Asymptotically Unbounded Buffers 7.2 Rare Events for Queuing Systems with Unbounded Buffers Part II Hitting Times and Phase Space Reduction for Perturbed Semi-Markov Processes 8 Asymptotically Comparable Functions 8.1 Complete Families of Asymptotically Comparable Functions 8.1.1 Definitions for Families of Asymptotically Comparable Functions 8.1.2 Operating Rules for Asymptotically Comparable Functions 8.2 Examples of Complete Families of Asymptotically Comparable Functions 8.2.1 Asymptotically Comparable Power-Type Functions 8.2.2 Asymptotically Comparable Power-Exponential-Type Functions 8.2.3 Asymptotically Comparable Power-Logarithmic-Type Functions 9 Perturbed Semi-Markov Processes and Reduction of Phase Space 9.1 Perturbed Semi-Markov Processes 9.1.1 Perturbed Semi-Markov Processes 9.1.2 Perturbation Conditions 9.1.3 Additional Asymptotic Comparability Conditions 9.1.4 Perturbed Markov Chains 9.2 Removing of Virtual Transitions for Perturbed Semi-Markov Processes 9.2.1 Semi-Markov Processes with Removed Virtual Transitions 9.2.2 Perturbation Conditions for Semi-Markov Processes with Removed Virtual Transitions 9.3 One-State Reduction of Phase Space for Perturbed Semi-Markov Processes 9.3.1 A Procedure of One-Step Phase Space Reduction for Perturbed Semi-Markov Processes 9.3.2 Perturbation Conditions for Reduced Semi-Markov Processes 9.4 Recurrent Reduction of Phase Space for Perturbed Semi-Markov Processes 9.4.1 The Recurrent Phase Space Reduction Algorithm 9.4.2 Summary of Recurrent Phase Space Reduction Algorithm 10 Asymptotics of Hitting Times for Perturbed Semi-Markov Processes 10.1 Hitting Times for Perturbed Semi-Markov Processes 10.1.1 Hitting Times and Related Asymptotic Problems 10.1.2 Hitting Times and Reduced Perturbation Conditions for Semi-Markov Processes 10.1.3 Hitting Times for Semi-Markov Processes with Reduced Phase Spaces 10.1.4 Recurrent Relations for Distributions and Laplace Transforms of Hitting Times 10.2 Weak Asymptotics for Distributions of Hitting Times 10.2.1 Asymptotics for Hitting Probabilities 10.2.2 Weak Asymptotic for Distributions of Hitting Times for the Case Where the Initial State Belongs to Domain 10.2.3 Admissible Normalisation Functions and Phase Types of Limiting Distributions 10.3 Weak Asymptotics for Distributions of Return Times 10.3.1 Hitting and Return Times 10.3.2 Weak Asymptotics for Distributions of Hitting and Return Times 11 Asymptotics for Expectations of Hitting Times for Perturbed Semi-Markov Processes 11.1 Expectations of Hitting Times 11.1.1 Recurrent Relations for Expectations of HittingTimes 11.1.2 Recurrent Relations for Limits of Expectations of Hitting Times 11.2 Asymptotics of Expectations of Hitting Times 11.2.1 Asymptotics for Expectations of Hitting Times for the Case Where an Initial State Belongs to Domain 11.2.2 Conditions of Simultaneous Convergence for Distributions and Expectations of Hitting Times 11.3 Asymptotics for Expectations of Return Times 11.3.1 Asymptotic for Expectations of Hitting Times in the Case Where an Initial State Belongs to Domain D 11.3.2 Asymptotics of Expectations for Return Times to Domain D 12 Generalisations and Examples of Limit Theorems for Hitting Times 12.1 Generalisations of Limit Theorems for Hitting Times 12.1.1 More General Perturbation Conditions 12.1.2 More General Hitting Reward Functionals 12.2 Hitting Times for Perturbed Birth–Death-Type Semi-Markov Processes 12.2.1 Perturbed Birth–Death-Type Semi-Markov Processes 12.2.2 Phase Space Reduction for Perturbed Birth–Death-Type Semi-Markov Processes 12.3 Numerical Examples 12.3.1 An Example of Singularly Perturbed Semi-Markov Processes with Two-State Domain 12.3.2 A One-Step Asymptotic Reduction of Phase Space 12.3.3 Asymptotics for Distributions and Expectations of Hitting Times Limit Theorems for Randomly Stopped Stochastic Processes A.1 Functional Limit Theorems for Càdlàg Stochastic Processes A.1.1 Convergence of Càdlàg Stochastic Processes in Topology U A.1.2 Convergence of Càdlàg Stochastic Processes in Topology J A.1.3 Convergence of Step-Sum Processes with Independent Increments in Topology J A.2 Limit Theorems for Randomly Stopped Stochastic Processes and Superpositions of Stochastic Processes A.2.1 Convergence in Distribution for Randomly Stopped Stochastic Processes A.2.2 Convergence in Distribution for Superpositions of Càdlàg Processes A.2.3 Convergence of Superpositions of Càdlàg Processes in Topology J A.3 Supplementary Asymptotic Results A.3.1 Slutsky Theorem and Related Results A.3.2 Functional Analogues of Slutsky Theorem Methodological and Bibliographical Notes B.1 Methodological Notes B.2 General Bibliographical Remarks References Index