# [Maxima] Applying Ito's lemma

Andrei Zorine zoav1602 at gmail.com
Thu Jun 4 08:12:11 CDT 2009

```Hi, J.
Probably you need a translation of itovsn3 package available here
http://www.uic.nnov.ru/~zoav1/mac/sde-0.9.tar.gz

==== Sample output goes here =========
(%o1)                 mac/sde/sde.mac
(%i2) ItoInit(t,dt);
(%o2)                                DONE
(%i3) BrownSingle(w,w0);
(%o3)                                 w0
(%i4) ItoStatus();
---------------------
Summary of current structure
of stochastic differentials
- - - - - - - - - - -
Current second-order structure
of semimartingales differentials
[     dw  dt ]
[            ]
[ dw  dt  0  ]
[            ]
[ dt  0   0  ]
- - - - - - - - - - -
Current first-order structure
of semimartingale differentials
[          dw  dt ]
[                 ]
[ Drifts:  0   dt ]
- - - - - - - - - - -
Current initial values:
[            w   t ]
[                  ]
[ Initials:  w0  0 ]
- - - - - - - - - - -
(%o4)                                true
(%i5) Itosde(f,df=(r+sigma_f*sigma_g)*f*dt+sigma_f*f*dw,f0);
(%o5)                         [DONE, DONE, DONE]
(%i6) ItoStatus();
---------------------
Summary of current structure
of stochastic differentials
- - - - - - - - - - -
Current second-order structure
of semimartingales differentials
[           df             dw       dt ]
[                                      ]
[         2        2                   ]
[ df  dt f  sigma_f   dt f sigma_f  0  ]
[                                      ]
[ dw   dt f sigma_f        dt       0  ]
[                                      ]
[ dt        0              0        0  ]
- - - - - - - - - - -
Current first-order structure
of semimartingale differentials
[                       df               dw  dt ]
[                                               ]
[ Drifts:  dt (f sigma_f sigma_g + f r)  0   dt ]
- - - - - - - - - - -
Current initial values:
[            f   w   t ]
[                      ]
[ Initials:  f0  w0  0 ]
- - - - - - - - - - -
(%o6)                                true
(%i7) ItoD(log(f));
df
(%o7)                               ------
log(f)

==== End of sample output ====

Is this what you expect?

--
Andrei Zorine

В сообщении от Thursday 04 June 2009 16:17:00 Julien Martin написал(а):
> Hello,
> I am relatively new to Maxima and I would like to apply Ito's lemma to ln(f)
> with f defined as follows:
>
> *df:=(r + sigma_f * sigma_g) f dt +(sigma_f ) f dz*
>
> Here is what I tried:
>
> *g(f,t):=log(f(t));
>
> (diff(g(f,t),f(t),1)*(r + sigma_f * sigma_g) + diff(g(f,t),t,2) + 1/2*
> diff(g(f,t),f(t),2)*(sigma_f * f(t))^2)*dt + diff(g(f,t),f(t),1)*(sigma_f *
> f(t))*dz;*
>
>
> I don't get what I want i.e. I it does not seem to derive. What I am getting
> wrong in the syntax?
>