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

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  • Ding, Xiaodong
  • Wu, Rangquan

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.

Suggested Citation

  • Ding, Xiaodong & Wu, Rangquan, 1998. "A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 155-171, November.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:2:p:155-171
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    References listed on IDEAS

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    1. Geiß, Christel & Manthey, Ralf, 1994. "Comparison theorems for stochastic differential equations in finite and infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 23-35, September.
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    Cited by:

    1. Jackson Loper, 2020. "Uniform Ergodicity for Brownian Motion in a Bounded Convex Set," Journal of Theoretical Probability, Springer, vol. 33(1), pages 22-35, March.
    2. Vladislav Krasin & Ivan Smirnov & Alexander Melnikov, 2018. "Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes," Annals of Finance, Springer, vol. 14(2), pages 195-209, May.

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