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The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Markov processes --- Stochastic integral equations --- Markoff processes --- Markov [Processus de ] --- Markov models --- Markov processen --- Markov-processen --- Processus de Markov --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Markov processes. --- Stochastic integral equations. --- Integral equations --- Stochastic analysis --- Analysis, Markov --- Chains, Markov --- Markov analysis --- Markov chains --- Models, Markov --- Processes, Markov --- Stochastic processes