The linear stochastic heat equation with Hermite noise

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The linear stochastic heat equation with Hermite noise

机译：具有Hermite噪声的线性随机热方程

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We analyze the solution to the linear stochastic heat equation driven by a multiparameter Hermite process of order q >= 1. This solution is an element of the qth Wiener chaos. We discuss various properties of the solution, such as the necessary and sufficient condition for its existence, self-similarity, alpha-variation and regularity of its sample paths. We will also focus on the probability distribution of the solution, which is non-Gaussian when q >= 2.

机译：我们将解决方案分析到由Q> = 1.该解决方案是Qth Wiener混沌的一个元素。我们讨论了解决方案的各种性质，例如其存在，自相似性，α-变异和其样本路径的必要条件。我们还将专注于解决方案的概率分布，当Q> = 2时是非高斯的概率分布。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2019年第3期|共23页
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正文语种 eng
中图分类物理学;
关键词
Wiener chaos; stochastic heat equation; Hermite process; Rosenblatt process; fractional Brownian motion; multiple stochastic integrals; cumulants; self-similarity; multiparameter stochastic processes;

机译：Wiener混乱;随机热方程;Hermite过程;Rosenblatt进程;分数褐色运动;多次随机积分;累积剂;自相同;多游戏随机过程;

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2. Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion [J] . Mohamed A.El-Beltagy, Noha A.Al-Mulla Journal of applied mathematics . 2014,第1期

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3. EFFECTS OF THE NOISE LEVEL ON NONLINEAR STOCHASTIC FRACTIONAL HEAT EQUATIONS [J] . Li Kexue Discrete and continuous dynamical systems . 2019,第10期

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4. Numerical Solution of Stochastic Nonlinear Differential Equations using Wiener-Hermite Expansion [C] . A. S. Al-Johani, M. A. El-Beltagy International Conference of Numerical Analysis and Applied Mathematics . 2014

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5. Applications of the Gaussian stochastic analysis of fractional Brownian noise to regularity of stochastic heat equations and to portfolio optimization. [D] . Sarol, Yalcin. 2005

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7. Remarks on non-linear noise excitability of some stochastic heat equations [O] . Foondun Mohammud, Joseph Mathew 2014

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The linear stochastic heat equation with Hermite noise

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