Abstract We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes.

中文翻译：

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纯非泊松跳跃随机微分方程的浓度不等式

摘要 我们为纯不必要泊松跳跃的随机微分方程的解提供了浓度不等式。我们的证明基于具有随机强度的点过程的平方可积泛函的运输成本不等式和关于半鞅的随机微积分元素。我们将一般结果应用于由更新和非线性霍克斯点过程驱动的随机微分方程的解。