论文标题
由纯跳跃噪声驱动的时间分数随机微分方程
Time fractional stochastic differential equations driven by pure jump Lévy noise
论文作者
论文摘要
在本文中，我们介绍了由纯跳跃lévy噪声驱动的可变订单时间分数差分方程，该方程模拟了表现出记忆效应的粒子运动。我们通过使用截断参数在初始条件和大跳跃系数上假设任何可集成性条件的情况下证明了该方程的良好性。在某些额外的条件下，我们还获得了解决方案的一些$ l^p $时刻估计。作为时刻估计的应用，我们证明了解决方案的Hölder规律性。
In this paper we introduce a variable order time fractional differential equation driven by pure jump Lévy noise, which models the motion of a particle exhibiting memory effect. We prove the well-posedness of this equation without assuming any integrability condition on the initial condition and the large jump coefficient, by using a truncation argument. Under some extra conditions, we also derive some $L^p$ moment estimates on the solutions. As an application of moment estimates, we prove the Hölder regularity of the solutions.
