A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales

Xiaodong Ding and Rangquan Wu

Stochastic Processes and their Applications, 1998, vol. 78, issue 2, 155-171

Abstract: By the local time method we prove comparison theorems for systems of stochastic differential inequalities with respect to semimartingales. Furthermore, we construct the 'maximal/minimal solution' of a system of stochastic differential inequalities by the monotone iterative technique. In one-dimensional case, using the comparison results, we give a stochastic Bihari-type inequality and its application to multi-dimensional stochastic differential equations.

Keywords: Stochastic; differential; inequality; Comparison; theorem; Semimartingale; Monotone; iteration (search for similar items in EconPapers)
Date: 1998
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