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Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations

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  • Peng, Shige
  • Zhu, Xuehong

Abstract

In this paper, we present a new approach to obtain the comparison theorem of two 1-dimensional SDEs with diffusion and jumps. The two equations is treated as one two-dimensional SDE and the comparison requirement is regarded as to keep the solution within the constraint . We then apply a new criteria of "viability condition" which is a necessary and sufficient condition to keep the solution to be inside the constraint K.

Suggested Citation

  • Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:3:p:370-380
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