Re: f'[t]== x[t]+u[t] ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg51612] Re: f'[t]== x[t]+u[t] ?*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Wed, 27 Oct 2004 01:54:28 -0400 (EDT)*Organization*: Uni Leipzig*References*: <clcnpn$q4m$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, you have to derive a Fokker-Planck equation from your stochastic ode and solve this one and you need some assumptions about the character of the noise (white noise ?) Regards Jens "ames kin" <ames_kin at yahoo.com> schrieb im Newsbeitrag news:clcnpn$q4m$1 at smc.vnet.net... >I was thinking about solving that using Mathematica. Clearly I do not have > enough math background. I wanted to get some feedbacks from the group. > > let, > > f'[t]== x[t]+u[t] where u[t] is the noise term. or fluctuation term. > > When you have a system with noise present, ( as in stochastic ode) is > it Ok or acceptable to obtain the deterministic solution in the form > of Mathematica InterpolatingFunction, and then add the noise when you > Evaluate > the InterpolatingFunction. > > ie, > > << Graphics`Colors` > << Graphics`Graphics` > > sol = NDSolve[{Derivative[3][y][x] + Derivative[2][y][x] + > Derivative[1][y][x] == -y[x]^3, y[0] == 1, Derivative[1][y][0] == > Derivative[2][y][0] == 0}, y, {x, 0, 20}]; > > which outputs an interpolating function which has to be "evaluated" > before it can be plotted. If so, If I throw in fluctuation as one > Table the evaluation, it will have an appearance of wide fluctuation. > > so, > > Table[Evaluate[y[x] /. sol[[1]]] + Random[Real, {-0.3, 0.3}], {x, 0, > 20, 0.2}] > > which then can be plotted. > > ListPlot[Table[Evaluate[y[x] /. sol[[1]]] + Random[Real, {-0.3, > 0.3}], {x, 0, 20, 0.2}], PlotStyle -> {GrayLevel[0.8]}, PlotJoined -> > True, PlotRange -> All, Axes -> False, Frame -> True, DisplayFunction > -> Identity]; > > What is wrong with this method of solution for a system such as > f'[t] == x[t] + u[t] ? (where u is the noise. this is my, most likely > erroneous, interpretation of stochastic ode) > > I mean, what is wrong with this method mathematically. > > thanks in advance for any feedback from the group. >