Ebook: Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory

This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory.

The aim of this book is to provide the reader with the theoretical and practical material necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields.

The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given.

The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions.

This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.

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This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory.

 

The aim of this book is to provide the reader with the theoretical and practical material necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields.

 

The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given.

 

The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions.

 

This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.

---

This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory.

 

The aim of this book is to provide the reader with the theoretical and practical material necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields.

 

The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given.

 

The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions.

 

This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.

Content:
Front Matter....Pages i-x
Definition of stochastic process. Cylinder ?-algebra, finite-dimensional distributions, the Kolmogorov theorem....Pages 1-10
Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions....Pages 11-19
Trajectories. Modifications. Filtrations....Pages 21-32
Continuity. Differentiability. Integrability....Pages 33-42
Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures....Pages 43-58
Gaussian processes....Pages 59-70
Martingales and related processes in discrete and continuous time. Stopping times....Pages 71-105
Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values....Pages 107-127
Prediction and interpolation....Pages 129-136
Markov chains: Discrete and continuous time....Pages 137-158
Renewal theory. Queueing theory....Pages 159-173
Markov and diffusion processes....Pages 175-192
It? stochastic integral. It? formula. Tanaka formula....Pages 193-213
Stochastic differential equations....Pages 215-228
Optimal stopping of random sequences and processes....Pages 229-240
Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems....Pages 241-270
Statistics of stochastic processes....Pages 271-302
Stochastic processes in financial mathematics (discrete time)....Pages 303-313
Stochastic processes in financial mathematics (continuous time)....Pages 315-326
Basic functionals of the risk theory....Pages 327-357
Back Matter....Pages 1-17

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This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory.

 

The aim of this book is to provide the reader with the theoretical and practical material necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields.

 

The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given.

 

The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions.

 

This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.

Content:
Front Matter....Pages i-x
Definition of stochastic process. Cylinder ?-algebra, finite-dimensional distributions, the Kolmogorov theorem....Pages 1-10
Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions....Pages 11-19
Trajectories. Modifications. Filtrations....Pages 21-32
Continuity. Differentiability. Integrability....Pages 33-42
Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures....Pages 43-58
Gaussian processes....Pages 59-70
Martingales and related processes in discrete and continuous time. Stopping times....Pages 71-105
Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values....Pages 107-127
Prediction and interpolation....Pages 129-136
Markov chains: Discrete and continuous time....Pages 137-158
Renewal theory. Queueing theory....Pages 159-173
Markov and diffusion processes....Pages 175-192
It? stochastic integral. It? formula. Tanaka formula....Pages 193-213
Stochastic differential equations....Pages 215-228
Optimal stopping of random sequences and processes....Pages 229-240
Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems....Pages 241-270
Statistics of stochastic processes....Pages 271-302
Stochastic processes in financial mathematics (discrete time)....Pages 303-313
Stochastic processes in financial mathematics (continuous time)....Pages 315-326
Basic functionals of the risk theory....Pages 327-357
Back Matter....Pages 1-17
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