Below code is used to solve a stochastic equation numerically in Mathematica for one particle. I wonder if there is a way to generalize it to the case of more than one particle and average over them. Is there anyone who knows how to do that?
Clear["Global`*"]
{ a = Pi, , b = 2 Pi, l = 5, k = 1};
ic = x@tbegin == 1;
tbegin = 1;
tend = 400;
interval = {1, 25};
lst := NestWhileList[(# + RandomVariate@TruncatedDistribution[interval,
StableDistribution[1, 0.3, 0, 0, 1]]) &, tbegin, # < tend &];
F[t_] := Piecewise[{{k, Or @@ #}}, -k] &[# <= t < #2 & @@@
Partition[lst, 2]];
eqn := x'[t] == (F@(t)) ;
sol = NDSolveValue[{eqn, ic}, x, {t, tbegin, tend},
MaxSteps -> Infinity];
Plot[sol@t, {t, tbegin, tend}]
First[First[sol]]
Plot[sol'[t], {t, tbegin, tend}]
Plot[F[t], {t, tbegin, tend}]