Solution Of Stochastic Integral Equation Research Articles

Zur Konstruktion eindimensionaler homogener Markoffscher Prozesse

The aim of this paper is the construction of a class of semi-groups of homogeneous onedimensional Markov processes with respect to a given infinitesimal operator. This is done namely by the method of stochastic integration represented in the book of Skorokhod. The Lipschitzian conditions — needed there — are weakened to uniform continuity by a method of approximation of semi-groups. Also to these semi-groups we can construct Markov processes as solutions of stochastic integral equations. The representation is connected with the result of Meyer, Watanabe, Motoo.