Stochastic differential equation Gompertz plotting a graph

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;

end

figure;

plot(t,x);

Answer 1

[Alan Stevens]

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

[George Hendry]

Thanks I'm not sure what the value of the dt is this model as I have seen various differing values of dt due to the weiner process do you have any views on what it should be?

[Torsten]

It's the "Wiener Process", not the "Weiner Process".