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Author: Robert M. Blumenthal Publisher: Springer Science & Business Media ISBN: 1468494120 Category : Mathematics Languages : en Pages : 287
Book Description
Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T
Author: Robert M. Blumenthal Publisher: Springer Science & Business Media ISBN: 1468494120 Category : Mathematics Languages : en Pages : 287
Book Description
Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T
Author: Kiyosi Itô Publisher: Springer ISBN: 981100272X Category : Mathematics Languages : en Pages : 54
Book Description
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m
Author: Ju-Yi Yen Publisher: Springer ISBN: 3319012703 Category : Mathematics Languages : en Pages : 140
Book Description
This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.
Author: Loïc Chaumont Publisher: Springer Nature ISBN: 3030833097 Category : Mathematics Languages : en Pages : 354
Book Description
This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.
Author: Marco Ferrante Publisher: Springer ISBN: 9783319128337 Category : Mathematics Languages : en Pages : 250
Book Description
This textbook will present, in a rigorous way, the basic theory of the discrete-time and the continuous-time Markov chains, along with many examples and solved problems. For both the topics a simple model, the Random Walk and the Poisson Process respectively, will be used to anticipate and illustrate the most interesting concepts rigorously defined in the following sections. A great attention will be paid to the applications of the theory of the Markov chains and many classical as well as new results will be faced in the book. This textbook is intended for a basic course on stochastic processes at an advanced undergraduate level and the background needed will be a first course in probability theory. A big emphasis is given to the computational approach and to simulations.
Author: L. C. G. Rogers Publisher: Cambridge University Press ISBN: 9780521775939 Category : Mathematics Languages : en Pages : 498
Book Description
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.
Author: Robert M. Blumenthal
Author: Robert M. Blumenthal
Author: Robert McCallum Blumenthal
Author: J. A. M. van der Weide
Author: Juha Vuolle-Apiala
Author: Kiyosi Itô
Author: Ju-Yi Yen
Author: Loïc Chaumont
Author: Thomas Stephenson Salisbury
Author: Marco Ferrante
Author: L. C. G. Rogers