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© 2004

The Theory of Stochastic Processes I

Book

Part of the Classics in Mathematics book series

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 1-49
  3. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 50-145
  4. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 146-194
  5. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 195-307
  6. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 308-361
  7. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 362-439
  8. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 440-524
  9. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorokhod
    Pages 525-557
  10. Back Matter
    Pages 558-574

About this book

Introduction

From the Reviews:

"Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection."
D.W. Stroock in Bulletin of the American Mathematical Society, 1980

"To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this ever-expanding field"
K.L. Chung in American Scientist, 1977

"..., the subject has grown enormously since 1953, and there will never be a true successor to Doob's book, but Gihman and Skorohod's three volumes will, I think, occupy a rather similar position as an invaluable tool of reference for all probability theorists. ... The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..."
J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977

Keywords

60-02 60Jxx 60Kxx YellowSale2006 stochastic processes Gaussian measure Gaussian process Markov chain Markov process Martingal Martingale probability probability theory random function Random variable Random Walk

Authors and affiliations

  1. 1.Institute of Applied Mathematics and MechanicsAcademy of Sciences of the Ukrainian SSRDonetskUSSR
  2. 2.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRKievUSSR

About the authors

Biography of I.I. Gikhman

Iosif Ilyich Gikhman was born on the 26th of May 1918 in the city of Uman, Ukraine. He studied in Kiev, graduating in 1939, then remained there to teach and do research under the supervision of N. Bogolyubov, defending a "candidate" thesis on the influence of random processes on dynamical systems in 1942 and a doctoral dissertation on Markov processes and mathematical statistics in 1955.

I.I. Gikhman is one of the founders of the theory of stochastic differential equations and also contributed significantly to mathematical statistics, limit theorems, multidimensional martingales, and stochastic control. He died in 1985, in Donetsk.

Biography of A.V. Skorokhod

Anatoli Vladimirovich Skorokhod was born on September 10th, 1930 in the city Nikopol, Ukraine. He graduated from Kiev University in 1953, after which his graduate studies at Moscow University, were directed by E.B. Dynkin.

From 1956 to 1964 Anatoli Skorokhod was a professor of Kiev university. Threafter he worked at the Institute of Mathematics of the Ukrainian Academy of Science, but he has also, since 1993, been professor of Statistics and Probability at Michigan State University.

Skorokhod was elected to the Ukrainian Academy of Sciences in 1985 and became a Fellow of American Academy of Arts and Sciences in 2000.

His mathematical research interests are the theory of stochastic processes, stochastic differential equations, Markov processes, randomly perturbed dynamical systems.

Bibliographic information

  • Book Title The Theory of Stochastic Processes I
  • Authors Iosif I. Gikhman
    Anatoli V. Skorokhod
  • Series Title Classics in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-61943-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-06573-9
  • Softcover ISBN 978-3-540-20284-4
  • eBook ISBN 978-3-642-61943-4
  • Series ISSN 1431-0821
  • Edition Number 1
  • Number of Pages VIII, 574
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as Vol. 210 in the series: Grundlehren der mathematischen Wissenschaften
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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