On Moment Estimates for Solutions of Mixed SDEs under Non-Lipschitz Condition

Xiao Xia SUN, Xuan Ming NI, Jun Yu ZHANG

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 393-404.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 393-404. DOI: 10.12386/A2022sxxb0031

On Moment Estimates for Solutions of Mixed SDEs under Non-Lipschitz Condition

  • Xiao Xia SUN1, Xuan Ming NI2, Jun Yu ZHANG3
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Abstract

We consider stochastic differential equations (SDEs) driven by mixed fractional Brownian motions under non-Lipschitz conditions. The mixed fractional Brownian motion is a linear combination of Brownian motion and fractional Brownian moiton. We give the p-th moment estimates and the continuity for solutions of considered SDEs by divergence-type Itô formula and Malliavin calculus for mixed fractional Brownianmotion.

Key words

fractional Brownian motion / mixed fractional Brownian motion / nonLipschitz conditions / p-th moment estimates / continuity

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Xiao Xia SUN, Xuan Ming NI, Jun Yu ZHANG. On Moment Estimates for Solutions of Mixed SDEs under Non-Lipschitz Condition. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 393-404 https://doi.org/10.12386/A2022sxxb0031

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