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全自动洗衣机怎么拆开清洗Stochastic differential equations driven by fractional Brownian motion with locally Lipschitz drift and their implicit Euler approximation 期刊名称： Proceedings of the Royal Society of Edinburgh Section A Mathematics 作者： Shao-Qin Zhang,Chenggui Yuan需要的英文
年份： 2020年
稀少期号： 第4期
忽图剌关键词： Locally Lipschitz drift;fractional Brownian motion;implicit Euler
scheme;optimal strong convergence rate;interest rate models;60H35;60H10损失惨重
摘要：In this paper, we study a class of one-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $ H \\gt
\\frac{{1}\\over{2}}$ . The drift term of the equation is locally Lipschitz and unbounded in the neighbourhood of the origin. We show the existence, uniqueness and positivity of the solutions. The estimates of moments, including the negative power moments, are given. We also develop the implicit
Euler scheme, proved that the scheme is positivity prerving and strong convergent, and obtain rate of convergence. Furthermore, by using Lamperti transformation, we show that our results can be applied to stochastic interest rate models such as mean-reverting stochastic volatility model and strongly nonlinear At-Sahalia type model.
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