Assuming you already have y, ymaybe, t and s:
if t > s
y = ymaybe; % ymaybe becomes the new y
else
pr = exp(-s + t);
my_randomnumber = rand;
if my_randomnumber < pr
y = ymaybe; % ymaybe becomes the new y with probability exp(-s+t)
end
end
The first part (t>s) is obvious. The second part is slightly tricky: whenever you want an event to happen with probability p, you simply draw a random number from a uniform distribution between 0 and 1 using rand function. Since the CDF of a uniform distribution U[0,1] grows linearly with unit slope, this random number will be less than p with probability p. Since you want to switch ymaybe for y with probability p, all you need to do is assign y=ymaybe if this random number is less than p. This trick can be handy in many places, so make sure you understand why this works.
