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14 produkter
14 produkter
Inbunden, Engelska, 2006
2 098 kr
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This book is an English translation of Kiyosi Ito's monograph published in Japanese in 1957. It gives a unified and comprehensive account of additive processes (or Levy processes), stationary processes, and Markov processes, which constitute the three most important classes of stochastic processes. Written by one of the leading experts in the field, this volume presents to the reader lucid explanations of the fundamental concepts and basic results in each of these three major areas of the theory of stochastic processes.With the requirements limited to an introductory graduate course on analysis (especially measure theory) and basic probability theory, this book is an excellent text for any graduate course on stochastic processes. Kiyosi Ito is famous throughout the world for his work on stochastic integrals (including the Ito formula), but he has made substantial contributions to other areas of probability theory as well, such as additive processes, stationary processes, and Markov processes (especially diffusion processes), which are topics covered in this book. For his contributions and achievements, he has received, among others, the Wolf Prize, the Japan Academy Prize, and the Kyoto Prize.
Häftad, Engelska, 1985
665 kr
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A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
Häftad, Engelska, 2014
704 kr
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The central and distinguishing feature shared by all the contributions made by K. Ito is the extraordinary insight which they convey. Reading his papers, one should try to picture the intellectual setting in which he was working. At the time when he was a student in Tokyo during the late 1930s, probability theory had only recently entered the age of continuous-time stochastic processes: N. Wiener had accomplished his amazing construction little more than a decade earlier (Wiener, N. , "Differential space," J. Math. Phys. 2, (1923)), Levy had hardly begun the mysterious web he was to eventually weave out of Wiener's P~!hs, the generalizations started by Kolmogorov (Kol mogorov, A. N. , "Uber die analytische Methoden in der Wahrscheinlichkeitsrechnung," Math Ann. 104 (1931)) and continued by Feller (Feller, W. , "Zur Theorie der stochastischen Prozesse," Math Ann. 113, (1936)) appeared to have little if anything to do with probability theory, and the technical measure-theoretic tours de force of J. L. Doob (Doob, J. L. , "Stochastic processes depending on a continuous parameter, " TAMS 42 (1937)) still appeared impregnable to all but the most erudite. Thus, even at the established mathematical centers in Russia, Western Europe, and America, the theory of stochastic processes was still in its infancy and the student who was asked to learn the subject had better be one who was ready to test his mettle.
Del 1203 - Lecture Notes in Mathematics
Stochastic Processes and Their Applications
Proceedings of the International Conference held in Nagoya, July 2-6, 1985
Häftad, Engelska, 1986
384 kr
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Inbunden, Engelska, 2004
815 kr
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The volume Stochastic Processes by K. Itö was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lévy-It ö decomposition of additive processes. Encouraged by Professor It ó we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran dom variables are treated using the dispersion as a main tooI. Lévy's form of characteristic functions of infinitely divisible distributions and basic proper ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the orem describes the decomposition of sample functions of additive processes, known today as the Lévy-Itó decomposition. This is thoroughly treated, as suming no continuity property in time, in a form close to the original 1942 paper of Itó, which gave rigorous expression to Lévy's intuitive understanding of path behavior.
E-bok
PDF, Engelska, 2006427 kr
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Häftad, Engelska, 1996
599 kr
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Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
Häftad, Engelska, 2010
653 kr
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The volume Stochastic Processes by K. Itö was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lévy-It ö decomposition of additive processes. Encouraged by Professor It ó we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran dom variables are treated using the dispersion as a main tooI. Lévy's form of characteristic functions of infinitely divisible distributions and basic proper ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the orem describes the decomposition of sample functions of additive processes, known today as the Lévy-Itó decomposition. This is thoroughly treated, as suming no continuity property in time, in a form close to the original 1942 paper of Itó, which gave rigorous expression to Lévy's intuitive understanding of path behavior.
E-bok
PDF, Engelska, 2012791 kr
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Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
Engelska, 2014
648 kr
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E-bok
PDF, Engelska, 2013840 kr
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The volume Stochastic Processes by K. Itö was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lévy-It ö decomposition of additive processes. Encouraged by Professor It ó we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran dom variables are treated using the dispersion as a main tooI. Lévy''s form of characteristic functions of infinitely divisible distributions and basic proper ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the orem describes the decomposition of sample functions of additive processes, known today as the Lévy-Itó decomposition. This is thoroughly treated, as suming no continuity property in time, in a form close to the original 1942 paper of Itó, which gave rigorous expression to Lévy''s intuitive understanding of path behavior.
Häftad, Engelska, 2015
707 kr
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Kosaku Yosida, born on February 7, 1909, was brought up in Tokyo. Having majored in Mathematics at University of Tokyo, he was appointed to Assistant at Osaka University in 1933 and promoted to Associate Professor in 1934. He re ceived the title of Doctor of Science from Osaka University in 1939. In 1942 he was appointed to Professor at Nagoya University, where he worked very hard with his colleagues to promote and expand the newly established Department of Mathe matics. He was appointed to Professor at Osaka University in 1953 and then to Professor at University of Tokyo in 1955. After retiring from University of Tokyo in 1969, he was appointed to Professor at Kyoto University, where he also acted as Director of the Research Institute for Mathematical Sciences. He retired from Kyoto University in 1972 and worked as Professor at Gakushuin University until 1979. Yosida acted as President of the Mathematical Society of Japan, as Member of the Science Council of Japan, and as Member of the Executive Committee of the International Mathematical Union. In 1967 he received the Japan Academy Prize and the Imperial Prize for his famous work on the theory of semigroups and its applications. In 1971 he was elected Member of the Japan Academy. Yosida went abroad many times to give series of lectures at mathematical in stitutions and to deliver invited lectures at international mathematical symposia.
Häftad, Engelska, 2016
546 kr
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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< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, Itô used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {a}. This theory of Itô's of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by Itô is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of Itô's beautiful and impressive lectures in his day.
E-bok
PDF, Engelska, 2015602 kr
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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< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, Itô used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {a}. This theory of Itô''s of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by Itô is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of Itô''s beautiful and impressive lectures in his day.