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Results tagged with stochastic-calculus
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user 26549
Questions about stochastic calculus in Mathematica, for example how to use ItoProcess and RandomFunction.
1
vote
1
answer
533
views
Ito process for 2D system
I have the following 2D dynamical system that I solve with NDSolve:
q[v_,x_]:=-v+c Tanh[3*v]-Sign[x];
sol = NDSolve[{x'[t] == v[t],
v'[t] == q[x[t],v[t]], x[0] == 0.01,
v[0] == 0.01}, {x[t], …
- 2,117
1
vote
2
answers
99
views
Changing a set of ODE to SDE's
I'm trying to add noise to a system I have of ODE's which I solve using NDSolveValue
It is written as follows (I did not specify here the functions as they are lengthy, and I'd like to keep the questi …
- 2,117
2
votes
0
answers
55
views
Monitoring time step manually within RandomFunction
Consider the following stochastic differential equation
Ie = 0.5; a = 0.7; b = 0.8; \[Tau] = 12.5;
q[v_, w_] := v - v^3/3 - w + Ie;
p[v_, w_] := 1/\[Tau] (v + a - b w);
\[Sigma] = 1;
sol2 = RandomFu …
- 2,117
3
votes
1
answer
274
views
Solving a stochastic dynamical system
I'm attempting to add gaussian white noise into a single equation of a 2 state variable dynamical system
$$\frac{dx(t)}{dt}=1-x(t)\left(1+e^{-y(t)}\right)$$
$$\frac{dy(t)}{dt}=1-y(t)\left(1+e^{\frac{x …
- 2,117
3
votes
1
answer
378
views
Stochastic ODE Integration problems using RandomFunction
I'm attempting to add noise to a set of ODE's with two state variables.
$$\frac{dx}{dt} = 10 -(x-1)\left(1+\frac{exp\left(\frac{x-1}{5y}\right)}{50y}\right)$$
$$\frac{dy}{dt} = 2(1-y) -y\cdot exp\left …
- 2,117
4
votes
2
answers
583
views
Adding conditions to stochastic differential equations
Consider the following process
dt=0.001; s=1; tf=10;
f[x_, y_] := 2 - x^2;
g[x_, y_] := y - x y^2;
sol = RandomFunction[ItoProcess[{
\[DifferentialD]x[t] ==
f[x[t], y …
- 2,117