Branching Random Walks in Nonhomogenous Environments
2013
John Wiley & Sons Inc (Hersteller)
9781118569375 (ISBN)
John Wiley & Sons Inc (Hersteller)
9781118569375 (ISBN)
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Devoted to the theory of branching random walks, describing the finite branching one-source environment, gradually increasing the complexity of the model Explores the branching random walk by means of the spectral methods. Exemplifies application of the Tauberian theorems in the asymptotical problems of the probability theory.
The book is devoted to a modern section of the probability theory, the so-called theory of branching random walks. Chapter 1 describes the random walk model in the finite branching one-source environment. Chapter 2 is devoted to a model of homogeneous, symmetrical, irreducible random walk (without branching) with finite variance of the jumps on the multidimensional integer continuous-time lattice where transition is possible to an arbitrary point of the lattice and not only to the neighbor state. This model is a generalization of the simple symmetrical random walk often encountered in the applied studies. In Chapter 3 the branching random walk is studied by means of the spectral methods. Here, the property of monotonicity of the mean number of particles in the source plays an important role in the subsequent parts of the book. Chapter 4 demonstrates that existence of an isolated positive eigenvalue in the spectrum of unperturbed random walk generator defines the exponential growth of the process in the supercritical case. Chapter 5 exemplify application of the Tauberian theorems in the asymptotical problems of the probability theory.
At last, the final Chapters 6 and 7 are devoted to detailed examination of survival probabilities in the critical and subcritical cases.
The book is devoted to a modern section of the probability theory, the so-called theory of branching random walks. Chapter 1 describes the random walk model in the finite branching one-source environment. Chapter 2 is devoted to a model of homogeneous, symmetrical, irreducible random walk (without branching) with finite variance of the jumps on the multidimensional integer continuous-time lattice where transition is possible to an arbitrary point of the lattice and not only to the neighbor state. This model is a generalization of the simple symmetrical random walk often encountered in the applied studies. In Chapter 3 the branching random walk is studied by means of the spectral methods. Here, the property of monotonicity of the mean number of particles in the source plays an important role in the subsequent parts of the book. Chapter 4 demonstrates that existence of an isolated positive eigenvalue in the spectrum of unperturbed random walk generator defines the exponential growth of the process in the supercritical case. Chapter 5 exemplify application of the Tauberian theorems in the asymptotical problems of the probability theory.
At last, the final Chapters 6 and 7 are devoted to detailed examination of survival probabilities in the critical and subcritical cases.
1. Model Description and Basic Equations. 2. Random Walk without branching. 3. Spectral Classi&fication of the First Moments. 4. Limit Theorem for the Supercritical Case. 5. Moments in the Critical and Subcritical Cases. 6. Limit Theorems for the Critical Case. 7. Limit Theorems for the Subcritical Case.
| Reihe/Serie | ISTE |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 150 x 250 mm |
| Gewicht | 4433 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik | |
| ISBN-13 | 9781118569375 / 9781118569375 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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