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首页> 外文期刊>Stochastic Processes and Their Applications: An Official Journal of the Bernoulli Society for Mathematical Statistics and Probability >Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Levy noise
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Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Levy noise

机译：具有非高斯利维噪声的随机微分方程和半线性方程组的温和解的存在性

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摘要

Existence and uniqueness of the mild solutions for stochastic differential equations for Hilbert valued stochastic processes are discussed, with the Multiplicative noise term given by an integral with respect to a general compensated Poisson random measure. Parts of the results allow for coefficients which can depend on the entire past path of the solution process. In the Markov case Yosida approximations are also discussed, as well as continuous dependence on initial data, and coefficients. The case of coefficients that besides the dependence on the solution process have also an additional random dependence is also included in our treatment. All results are proven for processes with values in separable Hilbert spaces. Differentiable dependence on the initial condition is proven by adapting a method of S. Cerrai.
机译：讨论了希尔伯特值随机过程的随机微分方程的温和解的存在性和唯一性，其中乘积噪声项是由积分给出的，与一般的补偿泊松随机测度有关。部分结果允许系数取决于求解过程的整个过去路径。在马尔可夫案例中，还讨论了Yosida逼近，以及对初始数据和系数的连续依赖性。在系数的情况下，除了对求解过程的依赖性之外，还具有其他随机依赖性，这也包括在我们的处理中。对于具有可分离希尔伯特空间中的值的过程，所有结果都得到了证明。通过采用S. Cerrai的方法证明了对初始条件的可区分依赖性。

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