Stochastic differential equation Gompertz plotting a graph

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I have come stuck when entering the model which has a log(x(t) into my code and when looking at the Weiner process deciding what my value of dt would need to be. Because at the moment when producing the graph using this code it is blank and I don't understand why that is happening when I introduce the log(x(t)) as I get a graph when it isn't intrdocued.I have coded
th = 0.1;
mu = 0.3;
sig = 0.1;
dt = 1e-1 ;
t = 0:dt:50; % Time vector
x = zeros(1,length(t)); % Allocate output vector, set initial condition
rng(1); % Set random seed
for i = 1:length(t)-1
x(i+1) = x(i)+th*x(i)*dt-mu*x(i)*dt-mu*log(x(i))*dt+sig*sqrt(dt)*randn;

Accepted Answer

Alan Stevens
Alan Stevens on 26 Feb 2022
You have x(1) = 0, so log(x(1)) is -Inf, which means that subsequent values of x will be NaNs.

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