| 摘要: |
| 本文研究了G-布朗运动指数泛函的矩估计的问题.利用拉普拉斯变换的方法，获得了At=∫0texp （λ（Bs+μs）） ds （λ ∈ R+，μ ∈ R） n阶矩的上下界.利用对称随机游动构造G-布朗运动指数泛函离散化形式的方法，推广了Y=∫0∞exp （Bt+μt） dt p阶矩的上下界. |
| 关键词: G-布朗运动 次线性空间 G-正态分布 拉普拉斯变换 积分矩 |
| DOI： |
| 分类号:0211.6 |
| 基金项目:国家自然科学基金资助（11971101）. |
|
| THE MOMENTS OF EXPONENTIAL FUNCTIONAL OF G-BROWNIAN MOTION |
|
HU Xin-yu1, YAN Li-tan1, GUO Meng-fan2
|
|
1.Department of Statistics, College of Science, Donghua University, Shanghai 201620, China;2.Industrial and Commercial Bank of China, Shanghai Branch, Shanghai 200120, China
|
| Abstract: |
| In this note, we investigate the exponential functional of G-Brownian Motion.Based on the Laplace transform, we derive the upper bound and lower bound of At=∫0texp(λ(Bs + μs)) ds(λ ∈ R+, μ ∈ R). With the help of suitable symmetric random walks, we construct the approximation to G-Brownian Motion, then generalize the upper bound and lower bound of moments of Y=∫0∞exp(Bt + μt) dt. |
| Key words: G-Brownian motion nonlinear expectation space G-normal distribution laplace transform integral moments |
