Difference between revisions of "Team:UCL/Math/Equations"
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<p>This is for two given functions $a$ and $b$. Also where $B(t)$ is a Brownian motion. | <p>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</p> | $X$ is a solution to the above equation, given that X is a function or path, if it satisfies the following</p> | ||
| − | $$X(T)=\ | + | $$X(T)=\int_0^T \mu(t,X(t))dt $$ |
</div> | </div> | ||
Revision as of 14:40, 31 July 2015
Equations
Partial Differential Equations
Classification
Stochastic Differential Equations
The equations we would like to solve are in the form
$$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 $$