ABSOLUTE CONTINUITY AND SINGULARITY OF LOCALLY ABSOLUTELY CONTINUOUS PROBABILITY DISTRIBUTIONS. I

The second part of this study deals with criteria for the absolute continuity of measures for various classes of random processes, starting out from the general results in Part I. We consider processes with independent increments, semimartingales, multivariate point processes, Gaussian processes, Markov chains, and processes with a countable number of states. Bibliography: 33 titles.

[1]  J. H. Schuppen,et al.  Transformation of Local Martingales Under a Change of Law , 1974 .

[2]  Yu. M. Kabanov,et al.  Criteria of absolute continuity of measures corresponding to multivariate point processes , 1976 .

[3]  H. Kunita,et al.  On Square Integrable Martingales , 1967, Nagoya Mathematical Journal.

[4]  Thomas Kailath,et al.  ABSOLUTE CONTINUITY AND RADON-NIKODYM DERIVATIVES FOR CERTAIN MEASURES RELATIVE TO WIENER MEASURE' , 1971 .

[5]  R. LePage,et al.  Equivalence-singularity dichotomies from zero-one laws , 1972 .

[6]  S. Kakutani On Equivalence of Infinite Product Measures , 1948 .

[7]  T. Kailath,et al.  Radon-Nikodym Derivatives with Respect to Measures Induced by Discontinuous Independent-Increment Processes , 1975 .

[8]  J. Jacod Sur la construction des integrales stochastiques et les sous-espaces stables de martingales , 1977 .

[9]  L. A. Shepp,et al.  Conditions for absolute continuity between a certain pair of probability measures , 1970 .

[10]  A. N. Sirjaev,et al.  ON THE ABSOLUTE CONTINUITY OF MEASURES CORRESPONDING TO PROCESSES OF DIFFUSION TYPE RELATIVE TO A WIENER MEASURE , 1972 .

[11]  Steven Orey,et al.  Conditions for the absolute continuity of two diffusions , 1974 .

[12]  T. Kailath The Structure of Radon-Nikodym Derivatives with Respect to Wiener and Related Measures , 1971 .

[13]  W. Stout Almost sure convergence , 1974 .

[14]  On likelihood ratios of measures given by Markov chains , 1975 .

[15]  H. J. Engelbert,et al.  On absolute continuity and singularity of probability measures , 1980 .

[16]  L. Shepp Radon-Nikodym Derivatives of Gaussian Measures , 1966 .

[17]  J. Jacod,et al.  Caractéristiques locales et conditions de continuité absolue pour les semi-martingales , 1976 .

[18]  J. Jacod Un théorème de représentation pour les martingales discontinues , 1976 .

[19]  R Š Lipcer,et al.  ON THE QUESTION OF ABSOLUTE CONTINUITY AND SINGULARITY OF PROBABILITY MEASURES , 1977 .

[20]  C. Doléans-Dade,et al.  Quelques applications de la formule de changement de variables pour les semimartingales , 1970 .

[21]  Yu. V. Prokhorov Convergence of Random Processes and Limit Theorems in Probability Theory , 1956 .

[22]  I. V. Girsanov On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures , 1960 .

[23]  B. Grigelionis Random point processes and martingales , 1975 .