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1.

図書

図書
Julius S. Bendat
出版情報: New York : Wiley, c1998  xiii, 474 p. ; 24 cm
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Linear Systems, Random Data
Zero-Memory Nonlinear Systems
Direct and Reverse MI/SO
Techniques for Analysis and Identification of Nonlinear Systems
Parallel Linear and Nonlinear Systems
Determination of Physical Parameters with Memory in Nonlinear Systems
Nonlinear System Response Properties of a Naval Frigate from Measured Ocean Engineering Data
Nonlinear System Response Properties of a Naval Barge from Measured Ocean Engineering Data
Bilinear and Trilinear Systems
Input Output Relations for Bilinear and Trilinear Systems
References
Index
Glossary of Symbols
Linear Systems, Random Data
Zero-Memory Nonlinear Systems
Direct and Reverse MI/SO
2.

図書

図書
Yu.A. Davydov, M.A. Lifshits, N.V. Smorodina
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiii, 184 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 173
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3.

図書

図書
N.U. Prabhu
出版情報: New York : Springer, c1998  xvi, 206 p. ; 25 cm
シリーズ名: Applications of mathematics ; 15
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4.

図書

図書
D. Bosq
出版情報: New York ; Tokyo : Springer, c1998  xvi, 210 p. ; 24 cm
シリーズ名: Lecture notes in statistics ; 110
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5.

図書

図書
M.I. Freidlin, A.D. Wentzell ; translated by Joseph Szücs
出版情報: New York : Springer, 1998  xi, 430 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 260
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6.

図書

図書
Gregory F. Lawler, Lester N. Coyle
出版情報: Providence, R.I. : American Mathematical Society , [Princeton, N.J.] : Institute for Advanced Study, c1999  xii, 97 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 2 . IAS/Park City mathematical subseries
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7.

図書

図書
Thomas M. Liggett
出版情報: Berlin ; New York : Springer, c1999  xii, 332 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 324
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Background and Tools.- Contact Processes: Preliminaries
The Process on the Integer Lattice Zd
The Process on (1,...,N)d
The Process on the Homogeneous Tree Td
Notes and References.- Voter Models: Preliminaries
Models with General Threshold and Range
Models with Threshold = 1
Notes and References.- Exclusion Processes: Preliminaries
Asymmetric Processes on the Integers
Invariant Measures for Processes on (1,..,N)
The Tagged Particle Process.
Notes and References Bibliography.
Index.
Background and Tools.- Contact Processes: Preliminaries
The Process on the Integer Lattice Zd
The Process on (1,...,N)d
8.

図書

図書
by Uwe Franz and René Schott
出版情報: Dordrecht : Kluwer, c1999  vii, 227 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 490
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Preface
Introduction / 1:
Preliminaries on Lie groups / 2:
Hopf algebras, quantum groups and braided spaces / 3:
Stochastic Processes on quantum groups / 4:
Markov Structure of quantum Levy Processes / 5:
Diffusions on braided spaces / 6:
Evolution equations and Levy processes on quantum groups / 7:
Gauss Laws in the sense of Bernstein on quantum groups / 8:
Phase retrieval for probability distributions on quantum groups / 9:
Limit theorems on quantum groups / 10:
Bibliography
Index
Preface
Introduction / 1:
Preliminaries on Lie groups / 2:
9.

図書

図書
Tomasz Rolski ... [et al.]
出版情報: Chichester : J. Wiley, c1999  xviii, 654 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics
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Preface
List of Principal Notation
Concepts from Insurance and Finance / 1:
Introduction / 1.1:
The Claim Number Process / 1.2:
Renewal Processes / 1.2.1:
Mixed Poisson Processes / 1.2.2:
Some Other Models / 1.2.3:
The Claim Size Process / 1.3:
Dangerous Risks / 1.3.1:
The Aggregate Claim Amount / 1.3.2:
Comparison of Risks / 1.3.3:
Solvability of the Portfolio / 1.4:
Premiums / 1.4.1:
The Risk Reserve / 1.4.2:
Economic Environment / 1.4.3:
Reinsurance / 1.5:
Need for Reinsurance / 1.5.1:
Types of Reinsurance / 1.5.2:
Ruin Problems / 1.6:
Related Financial Topics / 1.7:
Investment of Surplus / 1.7.1:
Diffusion Processes / 1.7.2:
Equity Linked Life Insurance / 1.7.3:
Probability Distributions / 2:
Random Variables and Their Characteristics / 2.1:
Distributions of Random Variables / 2.1.1:
Basic Characteristics / 2.1.2:
Independence and Conditioning / 2.1.3:
Convolution / 2.1.4:
Transforms / 2.1.5:
Parametrized Families of Distributions / 2.2:
Discrete Distributions / 2.2.1:
Absolutely Continuous Distributions / 2.2.2:
Parametrized Distributions with Heavy Tail / 2.2.3:
Operations on Distributions / 2.2.4:
Some Special Functions / 2.2.5:
Associated Distributions / 2.3:
Distributions with Monotone Hazard Rates / 2.4:
Heavy-Tailed Distributions / 2.4.1:
Definition and Basic Properties / 2.5.1:
Subexponential Distributions / 2.5.2:
Criteria for Subexponentiality and the Class S / 2.5.3:
Pareto Mixtures of Exponentials / 2.5.4:
Detection of Heavy-Tailed Distributions / 2.6:
Large Claims / 2.6.1:
Quantile Plots / 2.6.2:
Mean Residual Hazard Function / 2.6.3:
Extreme Value Statistics / 2.6.4:
Premiums and Ordering of Risks / 3:
Premium Calculation Principles / 3.1:
Desired Properties of "Good" Premiums / 3.1.1:
Basic Premium Principles / 3.1.2:
Quantile Function: Two More Premium Principles / 3.1.3:
Ordering of Distributions / 3.2:
Concepts of Utility Theory / 3.2.1:
Stochastic Order / 3.2.2:
Stop-Loss Order / 3.2.3:
The Zero Utility Principle / 3.2.4:
Some Aspects of Reinsurance / 3.3:
Distributions of Aggregate Claim Amount / 4:
Individual and Collective Model / 4.1:
Compound Distributions / 4.2:
Definition and Elementary Properties / 4.2.1:
Three Special Cases / 4.2.2:
Some Actuarial Applications / 4.2.3:
Ordering of Compounds / 4.2.4:
The Larger Claims in the Portfolio / 4.2.5:
Claim Number Distributions / 4.3:
Classical Examples; Panjer's Recurrence Relation / 4.3.1:
Discrete Compound Poisson Distributions / 4.3.2:
Mixed Poisson Distributions / 4.3.3:
Recursive Computation Methods / 4.4:
The Individual Model: De Pril's Algorithm / 4.4.1:
The Collective Model: Panjer's Algorithm / 4.4.2:
A Continuous Version of Panjer's Algorithm / 4.4.3:
Lundberg Bounds / 4.5:
Geometric Compounds / 4.5.1:
More General Compound Distributions / 4.5.2:
Estimation of the Adjustment Coefficient / 4.5.3:
Approximation by Compound Distributions / 4.6:
The Total Variation Distance / 4.6.1:
The Compound Poisson Approximation / 4.6.2:
Homogeneous Portfolio / 4.6.3:
Higher-Order Approximations / 4.6.4:
Inverting the Fourier Transform / 4.7:
Risk Processes / 5:
Time-Dependent Risk Models / 5.1:
The Ruin Problem / 5.1.1:
Computation of the Ruin Function / 5.1.2:
A Dual Queueing Model / 5.1.3:
A Risk Model in Continuous Time / 5.1.4:
Poisson Arrival Processes / 5.2:
Homogeneous Poisson Processes / 5.2.1:
Compound Poisson Processes / 5.2.2:
Ruin Probabilities: The Compound Poisson Model / 5.3:
An Integro-Differential Equation / 5.3.1:
An Integral Equation / 5.3.2:
Laplace Transforms, Pollaczek-Khinchin Formula / 5.3.3:
Severity of Ruin / 5.3.4:
Bounds, Asymptotics and Approximations / 5.4:
The Cramer-Lundberg Approximation / 5.4.1:
Subexponential Claim Sizes / 5.4.3:
Approximation by Moment Fitting / 5.4.4:
Ordering of Ruin Functions / 5.4.5:
Numerical Evaluation of Ruin Functions / 5.5:
Finite-Horizon Ruin Probabilities / 5.6:
Deterministic Claim Sizes / 5.6.1:
Seal's Formulae / 5.6.2:
Exponential Claim Sizes / 5.6.3:
Renewal Processes and Random Walks / 6:
The Renewal Function; Delayed Renewal Processes / 6.1:
Renewal Equations and Lorden's Inequality / 6.1.3:
Key Renewal Theorem / 6.1.4:
Another Look at the Aggregate Claim Amount / 6.1.5:
Extensions and Actuarial Applications / 6.2:
Weighted Renewal Functions / 6.2.1:
A Blackwell-Type Renewal Theorem / 6.2.2:
Approximation to the Aggregate Claim Amount / 6.2.3:
Lundberg-Type Bounds / 6.2.4:
Random Walks / 6.3:
Ladder Epochs / 6.3.1:
Random Walks with and without Drift / 6.3.2:
Ladder Heights; Negative Drift / 6.3.3:
The Wiener-Hopf Factorization / 6.4:
General Representation Formulae / 6.4.1:
An Analytical Factorization; Examples / 6.4.2:
Ladder Height Distributions / 6.4.3:
Ruin Probabilities: Sparre Andersen Model / 6.5:
Formulae of Pollaczek-Khinchin Type / 6.5.1:
Compound Poisson Model with Aggregate Claims / 6.5.2:
Markov Chains / 6.5.5:
Initial Distribution and Transition Probabilities / 7.1:
Computation of the n-Step Transition Matrix / 7.1.2:
Recursive Stochastic Equations / 7.1.3:
Bonus-Malus Systems / 7.1.4:
Stationary Markov Chains / 7.2:
Long-Run Behaviour / 7.2.1:
Application of the Perron-Frobenius Theorem / 7.2.2:
Irreducibility and Aperiodicity / 7.2.3:
Stationary Initial Distributions / 7.2.4:
Markov Chains with Rewards / 7.3:
Interest and Discounting / 7.3.1:
Discounted and Undiscounted Rewards / 7.3.2:
Efficiency of Bonus-Malus Systems / 7.3.3:
Monotonicity and Stochastic Ordering / 7.4:
Monotone Transition Matrices / 7.4.1:
Comparison of Markov Chains / 7.4.2:
Application to Bonus-Malus Systems / 7.4.3:
An Actuarial Application of Branching Processes / 7.5:
Continuous-Time Markov Models / 8:
Homogeneous Markov Processes / 8.1:
Matrix Transition Function / 8.1.1:
Kolmogorov Differential Equations / 8.1.2:
An Algorithmic Approach / 8.1.3:
Monotonicity of Markov Processes / 8.1.4:
Phase-Type Distributions / 8.1.5:
Some Matrix Algebra and Calculus / 8.2.1:
Absorption Time / 8.2.2:
Operations on Phase-Type Distributions / 8.2.3:
Risk Processes with Phase-Type Distributions / 8.3:
The Compound Poisson Model / 8.3.1:
Numerical Issues / 8.3.2:
Nonhomogeneous Markov Processes / 8.4:
Construction of Nonhomogeneous Markov Processes / 8.4.1:
Application to Life and Pension Insurance / 8.4.3:
Markov Processes with Infinite State Space / 8.5:
Mixed Poisson Processes as Pure Birth Processes / 8.5.3:
The Claim Arrival Epochs / 8.5.4:
The Inter-Occurrence Times / 8.5.5:
Examples / 8.5.6:
Martingale Techniques I / 9:
Discrete-Time Martingales / 9.1:
Fair Games / 9.1.1:
Filtrations and Stopping Times / 9.1.2:
Martingales, Sub- and Supermartingales / 9.1.3:
Life-Insurance Model with Multiple Decrements / 9.1.4:
Convergence Results / 9.1.5:
Optional Sampling Theorems / 9.1.6:
Doob's Inequality / 9.1.7:
The Doob-Meyer Decomposition / 9.1.8:
Change of the Probability Measure / 9.2:
The Likelihood Ratio Martingale / 9.2.1:
Kolmogorov's Extension Theorem / 9.2.2:
Exponential Martingales for Random Walks / 9.2.3:
Simulation of Ruin Probabilities / 9.2.4:
Martingale Techniques II / 10:
Continuous-Time Martingales / 10.1:
Stochastic Processes and Filtrations / 10.1.1:
Stopping Times / 10.1.2:
Brownian Motion and Related Processes / 10.1.3:
Uniform Integrability / 10.1.5:
Some Fundamental Results / 10.2:
Ruin Probabilities and Martingales / 10.2.1:
Ruin Probabilities for Additive Processes / 10.3.1:
Law of Large Numbers for Additive Processes / 10.3.2:
An Identity for Finite-Horizon Ruin Probabilities / 10.3.4:
Piecewise Deterministic Markov Processes / 11:
Markov Processes with Continuous State Space / 11.1:
Transition Kernels / 11.1.1:
The Infinitesimal Generator / 11.1.2:
Dynkin's Formula / 11.1.3:
The Full Generator / 11.1.4:
Construction and Properties of PDMP / 11.2:
Behaviour between Jumps / 11.2.1:
The Jump Mechanism / 11.2.2:
The Generator of a PDMP / 11.2.3:
An Application to Health Insurance / 11.2.4:
The Compound Poisson Model Revisited / 11.3:
Exponential Martingales via PDMP / 11.3.1:
Cramer-Lundberg Approximation / 11.3.2:
A Stopped Risk Reserve Process / 11.3.4:
Characteristics of the Ruin Time / 11.3.5:
Compound Poisson Model in an Economic Environment / 11.4:
A Discounted Risk Reserve Process / 11.4.1:
The Adjustment Coefficient / 11.4.3:
Decreasing Economic Factor / 11.4.4:
Exponential Martingales: the Sparre Andersen Model / 11.5:
Backward Markovization Technique / 11.5.1:
Forward Markovization Technique / 11.5.3:
Point Processes / 12:
Stationary Point Processes / 12.1:
Palm Distributions and Campbell's Formula / 12.1.1:
Ergodic Theorems / 12.1.3:
Marked Point Processes / 12.1.4:
Ruin Probabilities in the Time-Stationary Model / 12.1.5:
Mixtures and Compounds of Point Processes / 12.2:
Nonhomogeneous Poisson Processes / 12.2.1:
Cox Processes / 12.2.2:
Compounds of Point Processes / 12.2.3:
Comparison of Ruin Probabilities / 12.2.4:
The Markov-Modulated Risk Model via PDMP / 12.3:
A System of Integro-Differential Equations / 12.3.1:
Law of Large Numbers / 12.3.2:
The Generator and Exponential Martingales / 12.3.3:
Periodic Risk Model / 12.3.4:
The Bjork-Grandell Model via PDMP / 12.5:
General Results / 12.5.1:
Poisson Cluster Arrival Processes / 12.6.2:
Superposition of Renewal Processes / 12.6.3:
The Markov-Modulated Risk Model / 12.6.4:
The Bjork-Grandell Risk Model / 12.6.5:
Diffusion Models / 13:
Stochastic Differential Equations / 13.1:
Stochastic Integrals and Ito's Formula / 13.1.1:
Levy's Characterization Theorem / 13.1.2:
Perturbed Risk Processes / 13.2:
Modified Ladder Heights / 13.2.1:
Other Applications to Insurance and Finance / 13.2.3:
The Black-Scholes Model / 13.3.1:
Stochastic Interest Rates in Life Insurance / 13.3.2:
Simple Interest Rate Models / 13.4:
Zero-Coupon Bonds / 13.4.1:
The Vasicek Model / 13.4.2:
The Cox-Ingersoll-Ross Model / 13.4.3:
Distribution Tables
References
Index
Preface
List of Principal Notation
Concepts from Insurance and Finance / 1:
10.

図書

図書
Albert N. Shiryaev ; translated from the Russian by N. Kruzhilin
出版情報: Singapore : World Scientific, c1999  xvi, 834 p. ; 23 cm
シリーズ名: Advanced series on statistical science & applied probability ; vol. 3
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