Random draws from conditional multinomial distribution
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I have to simulate data for 100 agents over 10,000 time periods for a variable, x. The initial value of x at time 0 for all agents is 0. The distribution of is a multinomial distribution, conditional on the past period's value, . Basically, can remain unchanged with probability 0.2, increase by 2571 with probability 0.5, increase by 2571*2 with probability 0.2, and increase by 2571*3 with probability 0.1, at any period. can never be lower than . How do I generate random values for this distribution?
I have tried:
x = mnrnd()
command, but I can't fit it to these specifications. Any help would be greatly appreciated!