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<p>The present paper investigates the existence and uniqueness of solutions to a class of stochastic differential equations driven by <i>G</i>-Brownian motion with non-Lipschitz drift. We assume the coefficient of the drift term is semi-monotone and the coefficients of volatility and quadratic variation terms are Lipschitz continuous. We prove the existence of solution for these equations by utilizing Yosida approximations. We also prove the exponential stability of solutions in the <i>p</i>-th moment. We apply our results in an example from the field of population dynamics.</p>

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Stochastic differential equations with G-Brownian motion and monotone coefficients

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • Fariba Pourrahimi,
  • Erfan Salavati,
  • S. Ali MirHassani

摘要

The present paper investigates the existence and uniqueness of solutions to a class of stochastic differential equations driven by G-Brownian motion with non-Lipschitz drift. We assume the coefficient of the drift term is semi-monotone and the coefficients of volatility and quadratic variation terms are Lipschitz continuous. We prove the existence of solution for these equations by utilizing Yosida approximations. We also prove the exponential stability of solutions in the p-th moment. We apply our results in an example from the field of population dynamics.