One-dimensional diffusion processes and their boundaries
Abstract
It is recalled how one-dimensional homogeneous diffusion processes can be constructed from the Wiener process via a time change and a space transformation.No Lipschitz requirements of the drift coefficient and of the diffusion coefficient as functions of the space variable are needed for this construction to be valid.The process constructed in this way will be the unique weak solution of the corresponding stochastic differential equation.Furthermore, a complete classification of boundary types and boundary behaviour is a direct result of the construction.The boundary behaviour of one-dimensional diffusion processes is illustrated by examples, in particular this boundary behaviour is discussed for a population model recently proposed by Lungu and 0ksendal.
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