| 一类高阶热方程解的随机计算 |
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| 引用本文： | 李志阐,王过京. 一类高阶热方程解的随机计算[J]. 河北大学学报(自然科学版), 1992, 0(2) |
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| 作者姓名： | 李志阐 王过京 |
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| 作者单位： | 河北大学(李志阐)，河北大学(王过京) |
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| 摘 要： | 本文给出一类“马氏过程”A-过程的随机积分的定义,证明随机积分的存在性及A过程函数的IT(?)公式。应用IT(?)公式给出一类高阶热方程解的随机表达式。
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| 关 键 词： | 随机积分 IT(?)公式 随机解 |
Stochastic Calculus for Solutions of a Class of High Order Parabolic Equation |
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| Li Zhichan Wang Guojing. Stochastic Calculus for Solutions of a Class of High Order Parabolic Equation[J]. Journal of Hebei University (Natural Science Edition), 1992, 0(2) |
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| Authors: | Li Zhichan Wang Guojing |
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| Affiliation: | Hebei University |
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| Abstract: | In this paper, stochastic integrals for A-processes x(t); t≥0,related to the equations (?)u(t,x) = (-1)n+1 (?)2nu(t,x),n≥2, are introduced. ITO formula of a function ofA-process is proven.The stochastic solution of the following initial value problemis given in the formu(t,x) = Ex{(?)(X(t))} + Ex((?)0'f(t - r,X(r))dr} by using the ITO formula. |
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| Keywords: | Stochastic integral. ITO formula Stochastic solution. |
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