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首页> 外文期刊>Discrete and continuous dynamical systems >EXISTENCE-UNIQUENESS AND EXPONENTIAL ESTIMATE OF PATHWISE SOLUTIONS OF RETARDED STOCHASTIC EVOLUTION SYSTEMS WITH TIME SMOOTH DIFFUSION COEFFICIENTS
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EXISTENCE-UNIQUENESS AND EXPONENTIAL ESTIMATE OF PATHWISE SOLUTIONS OF RETARDED STOCHASTIC EVOLUTION SYSTEMS WITH TIME SMOOTH DIFFUSION COEFFICIENTS

机译：具有时间平滑扩散系数延迟随机演化系统的旋转随机演化系统的唯一性和指数估计

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摘要

In this paper, we study the existence-uniqueness and exponential estimate of the pathwise mild solution of retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. Firstly, the existence-uniqueness of the maximal local pathwise mild solution are given by the generalized local Lipschitz conditions, which extend a classical Pazy theorem on PDEs. We assume neither that the noise is given in additive form or that it is a very simple multiplicative noise, nor that the drift coefficient is global Lipschitz continuous. Secondly, the existence-uniqueness of the global pathwise mild solution are given by establishing an integral comparison principle, which extends the classical Wintner theorem on ODEs. Thirdly, an exponential estimate for the pathwise mild solution is obtained by constructing a delay integral inequality. Finally, the results obtained are applied to a retarded stochastic infinite system and a stochastic partial functional differential equation. Combining some known results, we can obtain a random attractor, whose condition overcomes the disadvantage in existing results that the exponential converging rate is restricted by the maximal admissible value for the time delay.
机译：本文研究了希尔伯特值褐色运动驱动的延迟随机演化系统的存在唯一性和指数估计。首先，通过广义的局部嘴唇尖端条件给出最大局部PathWise温和溶液的存在 - 唯一性，其在PDE上延伸了一种经典的七大定理。我们假设噪声不在添加形式中或者是一个非常简单的乘法噪声，也不是漂移系数是全球嘴唇尖端的连续。其次，通过建立积分的比较原理给出全局途径温和溶液的存在唯一性，其在杂物中延伸了经典的Wintner定理。第三，通过构建延迟积分不等式来获得用于PathWise轻度溶液的指数估计。最后，获得的结果应用于延迟的随机无限系统和随机偏函数微分方程。结合一些已知结果，我们可以获得随机吸引子，其条件克服了现有结果中的缺点，即指数收敛速率受到时间延迟的最大可允许值的限制。

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