随机偏微分方程

这些研究成果使我们能够给出一类拟线性随机偏微分方程解的概率表示，从而扩展了线性随机偏微分方程的Feynman-Kac公式。

These research allow us to produce a probabilistic representation of certain quasi-linear stochastic partial differential equations , thus extending the Feynman-Kac formula for linear SPDEs .

有限差分方法与随机偏微分方程的数值模拟

Finite Difference Method and Numerical Simulation of Stochastic Partial Differential Equations

带跳的无穷维随机偏微分方程的逐次逼近

Successive approximations of infinite dimensional SPDEs with jump

本文讨论了可分Hilbert空间有限时滞非线性随机时滞偏微分方程能量解的指数稳定性。

This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces .

本文利用随机分析，偏微分方程和广义Ito公式探讨了跳&扩散过程下的回望期权的定价问题。

This paper mostly studies one of the valuations of floating strike price lookback options in a jump-diffusion model , by using the stochastic analysis , partial differential equation and general Ito formula .

40岁的巴尔加瓦博士在几何数论、尤其是质数上找到了一些新方法，而38岁的海瑞尔博士在研究随机噪声对偏微分方程的影响时取得了进展，捕捉到了湍流对洋流或飞机机翼周围空气流动的影响。

Dr. Bhargava , 40 , was recognized for new methods in the geometry of numbers , especially prime numbers , and Dr. Hairer , 38 , made advances in the study of the effect of random noise on partial differential equations , capturing the effect of turbulence on ocean currents or the flow of air around airplane wings .

并利用随机微分方程和偏微分方程之间的关系，对股票投资风险进行了估计，得到关于风险指标的动态轨线。

By using the relation between the stochastic , differential equations and the PDEs , we estimate the risk of investing stocks , and obtain the dynamic traces'of risk functions .

此模型可以避免传统随机微分方程中偏微分方程的繁琐求解过程及无封闭解的情况，方法简明易于操作，对认股权证定价理论的发展具有重要意义。

This model avoids the complicated solving process and the situation of no closed form solution of the partial differential equation in traditional stochastic differential equation . It will benefit the warranting pricing theory .

基于随机Fubini定理，将随机偏微分方程描述的Hopfield神经网络系统转化为用相应的随机常微分方程来描述。

Based on stochastic Fubini theorem , the Hopfield neural network system depicted by a stochastic partial differential equation is translated into a stochastic ordinary differential equation .

倒向随机微分方程在随机控制、偏微分方程、数理金融、经济等领域都有着广泛的应用。

From then on , BSDE is further studied and applied widely in stochastic control , partial differential equation ( PDE ), mathematical finance and economics .

我们认为带停时的倒向重随机微分方程也能给出一类拟线性随机偏微分方程的解的概率表示。

BDSDEs with stopping time are also very interesting to produce a probabilistic representation of certain quasi-linear stochastic partial differential equations .