Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet
Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet
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DOI：
10.1142/s0219493703000681
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发表时间：
2003-06
影响因子：
1.1
通讯作者：
M. Erraoui;Y. Ouknine;D. Nualart
中科院分区：
文献类型：
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作者：
M. Erraoui;Y. Ouknine;D. Nualart
设 为分数布朗片，赫斯特参数为 H，H′ ≤ 1/2。我们证明了一类具有 形式的加性分数布朗片的双曲随机偏微分方程的强解的存在性和唯一性，其中 b(z, x) 是满足某些增长和单调性假设的 Borel 函数。我们还证明了该方程的欧拉近似格式的收敛性。
Let be a fractional Brownian sheet with Hurst parameters H, H′ ≤ 1/2. We prove the existence and uniqueness of a strong solution for a class of hyperbolic stochastic partial differential equations with additive fractional Brownian sheet of the form , where b(ζ, x) is a Borel function satisfying some growth and monotonicity assumptions. We also prove the convergence of Euler's approximation scheme for this equation.