Strong comparison result for a class of reflected stochastic differential equations with non-Lipschitzian coefficients

Lijun Bo; Ruiming Yao

doi:10.1007/s11464-007-0005-6

Front. Math. China ›› 2007, Vol. 2 ›› Issue (1) : 73 -85. DOI: 10.1007/s11464-007-0005-6

Research Article

Strong comparison result for a class of reflected stochastic differential equations with non-Lipschitzian coefficients

Lijun Bo ¹^,²^,^a
, Ruiming Yao ¹

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Abstract

In this paper, we are concerned with a class of reflected stochastic differential equations (reflected SDEs) with non-Lipschitzian coefficients. Under the same coefficients assumptions as Fang and Zhang [Probab. Theory Relat. Fields, 2005, 132(3): 356–390] for a class of SDEs, we establish the pathwise uniqueness for the reflected SDEs. Furthermore, a strong comparison theorem is proved for the reflected SDEs in a one-dimensional case.

Keywords

reflected stochastic differential equations (reflected SDEs) / non-Lipschitzian coefficients / strong comparison theorem

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Lijun Bo, Ruiming Yao. Strong comparison result for a class of reflected stochastic differential equations with non-Lipschitzian coefficients. Front. Math. China, 2007, 2(1): 73-85 DOI:10.1007/s11464-007-0005-6

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