Stochastic processes : lectures given at Aarhus University /
Kiyosi Itō ; edited by Ole E. Barndorff-Nielsen, Ken-iti Satō.
- xii, 234 p. : ill. ; äc 24 cm.
Rev. ed. of: Stochastic processes, 1968/69. 1969.
Includes bibliographical references and index.
Additive processes (processes with independent increments) -- Definitions -- Decomposition of additive processes -- The Levy modification of additive processes continuous in probability -- Elementary Levy processes -- Fundamental lemma -- Structure of sample functions of Levy processes (a) -- Structure of sample functions of Levy processes (b) -- Three components of Levy processes -- Random point measures -- Homogeneous additive processes and homogeneous Levy processes -- Levy processes with increasing paths -- Stable processes -- Markov processes -- Transition probabilities and transition operators on compact metrizable spaces -- Summary of the Hille-Yosida theory of semi-groups -- Transition semi-group -- Probability law of the path -- Markov property -- The a-algebras B, B[subscript 1] and B(S) -- Strong Markov property -- An inequality of Kolmogorov type and its application -- Hitting times of closed sets -- Dynkin's formula -- Markov processes in generalized sense -- Examples -- Markov processes with a countable state space -- Fine topology -- Generator in generalized sense -- The Kac semi-group and its application to the Arcsine law -- Markov processes and potential theory -- Brownian motion and the Dirichlet problem. 1. 2.