Abstract
本文主要研究几何稳定过程的性质。首先，我们得到了由𝛼-𝑠𝑡𝑎𝑏𝑙𝑒过程驱动的几何稳定过程并给出几何稳定过程的解。其次，证明了在随机噪声较大时，几何稳定过程的解几乎处处以指数速率趋近于零。 The main purpose of this paper is to investigate the properties of geometric stable process. First, a model driven by 𝛼-𝑠𝑡𝑎𝑏𝑙𝑒 process is present. We obtain the solution of such model. Then, we prove that if the noise is sufficiently large, the solution of the geometric stable process will tend to zero at an exponential rate with probability one.
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