Sample paths of the solution to the fractional-colored stochastic heat equation
Sample paths of the solution to the fractional-colored stochastic heat equation
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DOI：
10.1142/s0219493717500046
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发表时间：
2015-01
影响因子：
1.1
通讯作者：
C. Tudor;Yimin Xiao
中科院分区：
文献类型：
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作者：
C. Tudor;Yimin Xiao
设{u（t，x），t ∈ [0，T]，x ∈ φ d}是具有相关空间结构的分数阶噪声驱动的线性随机热方程的解.我们分别研究了过程u关于时间和空间变量的各种路径性质。特别是，我们得到精确的一致连续模和Chung型重对数律。
Let {u(t,x),t ∈ [0,T],x ∈ ℝd} be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect to the time and to the space variable, respectively. In particular, we derive exact uniform moduli of continuity and Chung-type laws of iterated logarithm.