Team:UCL/Math/Equations

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Equations

Partial Differential Equations

Classification

Stochastic Differential Equations

The equations we would like to solve are in the form

$$dX=\mu(t, X(t))dt+\sigma(t,X(t))dB(t)$$

This is for two given functions $a$ and $b$. Also where $B(t)$ is a Brownian motion. $X$ is a solution to the above equation, given that X is a function or path, if it satisfies the following

$$X(T)=\int_0^T \mu(t,X(t))dt + \int_0^T \sigma(t,X(t))dB(t)$$