Yet again, here is a Springer volume that offers readers something completely new. Until now, solved examples of the application of stochastic control to actuarial problems could only be found in journals. Not any more: this is the first book to systematically present these methods in one volume. The author starts with a short introduction to stochastic control techniques, then applies the principles to several problems. These examples show how verification theorems and existence theorems may be proved, and that the non-diffusion case is simpler than the diffusion case. Schmidli's...
Yet again, here is a Springer volume that offers readers something completely new. Until now, solved examples of the application of stochastic cont...
Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various...
Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applicati...
The Poisson Dirichlet distribution, a probability on the in?nite-dimensional s- plex, was introduced by Kingman in 1975. Since then it has found applications in Bayesian statistics, combinatorics, number theory, ?nance, macroeconomics, physics and, especially, in population genetics. Several books have appeared that contain sections or chapters on the Poisson Dirichlet distribution. These include, but are not limited to, Aldous 2], Arratia, Barbour and Tavare 9], Ewens 67], Kingman 127, 130], and Pitman 155]. This book is the ?rst that focuses solely on the Poisson Dirichlet distribution...
The Poisson Dirichlet distribution, a probability on the in?nite-dimensional s- plex, was introduced by Kingman in 1975. Since then it has found appli...
The Poisson Dirichlet distribution, a probability on the in?nite-dimensional s- plex, was introduced by Kingman in 1975. Since then it has found applications in Bayesian statistics, combinatorics, number theory, ?nance, macroeconomics, physics and, especially, in population genetics. Several books have appeared that contain sections or chapters on the Poisson Dirichlet distribution. These include, but are not limited to, Aldous 2], Arratia, Barbour and Tavare 9], Ewens 67], Kingman 127, 130], and Pitman 155]. This book is the ?rst that focuses solely on the Poisson Dirichlet distribution...
The Poisson Dirichlet distribution, a probability on the in?nite-dimensional s- plex, was introduced by Kingman in 1975. Since then it has found appli...
A compact and rigorous treatment of measure-valued branching processes and immigration processes is given in the book at the level readable for graduate students. For the convenience of references, special attention has been paid to the generality of the framework. To develop a reasonably rich theory, the basic regularities of the models are certainly necessary.
In the first part of the book, the author not only constructs the transition semigroups of superprocesses with general spatial motions and branching mechanisms, but also proves the existence of their Borel right...
A compact and rigorous treatment of measure-valued branching processes and immigration processes is given in the book at the level readable for gra...
This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.
This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartinga...
Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the boundary and for dynamical systems there is a trap. The authors present the QSDs as the ones that allow describing the long-term behavior conditioned to not being killed. Studies in this research area started with Kolmogorov and Yaglom and in the last few decades have received a great deal of attention. The authors provide the exponential distribution property of the killing time for QSDs, present the more general result on their existence and...
Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the...
This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing this frequently overlooked relationship, the authors provide readers an entry point into several active areas, particularly applications related to general radiation transport. Cutting-edge research published in recent years is collected here for convenient reference. Organized into two parts, the first offers a modern perspective on the relationship between the neutron branching process (NBP) and the neutron transport equation (NTE), as well...
This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing...
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in...
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov c...
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in...
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov c...
