sdes.m

sdes.m

(* Stochastic Logistic Model Simulations (essentially just geometric Brownian motion) *)

M = 5000; (* Sample size *)
T = 5; (* Max time to simulate to *)

Datum1 = Table[2 RandomInteger[] - 1, {j, 1, M*T}];
Datum2 = Table[2 RandomInteger[] - 1, {j, 1, M*T}];
Datum3 = Table[2 RandomInteger[] - 1, {j, 1, M*T}];

B[t_, 1] := (1/Sqrt[M]) * Sum[Datum1[[j]], {j, 1, Floor[M*t]}];
B[t_, 2] := (1/Sqrt[M]) * Sum[Datum2[[j]], {j, 1, Floor[M*t]}];
B[t_, 3] := (1/Sqrt[M]) * Sum[Datum3[[j]], {j, 1, Floor[M*t]}];

Nr[t_, 1] := Exp[1/2 t + B[t, 1]];
Nr[t_, 2] := Exp[1/2 t + B[t, 2]];
Nr[t_, 3] := Exp[1/2 t + B[t, 3]];

Plot[{
  Nr[t, 1],
  Nr[t, 2],
  Nr[t, 3],
  Exp[t]
  }, {t, 0, T - .5},
 PlotRange -> Full,
 PlotTheme -> "Minimal",
 PlotStyle -> {
    {Blue, Thickness[0.0015]},
   {Magenta, Thickness[0.0015]},
   {Purple, Thickness[0.0015]}, {Red, Thickness[0.004]}
   }
 ]


(* Plot just some instance of Brownian Motion *)
Plot[B[t, 3], {t, 0, T}]