The Theory of Stochastic Processes I

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 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

• 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

• Institute of Applied Mathematics and Mechanics, Academy of Sciences of the Ukrainian SSR, Donetsk, USSR

  Iosif Il’ich Gihman

• Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev, USSR

  Anatoliĭ Vladimirovich Skorokhod

Biography of I.I. Gikhman

Iosif Ilyich Gikhman was born on the 26^th 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 10^th, 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.