linear recurrence relations with random coefficients Are there such things as recurrence equations with random variable coefficients. For example, $$W_n=W_{n-1}+F\cdot W_{n-1}$$ where $F$ is a random variable. I tried to see if I could make sense of it using the simplest possible case of $F$ being a uniform discrete random variable on 2 points but I didn't get far because even if the initial data is not random the succeeding terms in the sequence are and each term seems to live on a different space. I couldn't figure out what space $W_n$ and $W_{n-1}$ should live on. A google search turned up nothing for the obvious keywords "random recurrence equation".
Edit in response to Alekk's answer: More specifically suppose I wanted to find the probability $P(W_{200}>3000)$. Is there a way to compute the distribution of $W_{200}$ explicitly given the distribution of $F$ and some non-random initial data $W_0$?
Edit: $F$ does not depend on $n$ and to make things even more explicit lets say $F$ has the distribution $P(F=2f)=\dfrac{1}{2}, P(F=-f)=\dfrac{1}{2}$.
 A: So this is the product of IID random variables $1+F_n$, so you could take logarithms and do the more conventional sums of IID random variables $\log(1+F_n)$.  Perhaps the logarithms are complex numbers.
A: See the work of Viswanath on random Fibonacci sequences.
A: There are such things as probabilistic recurrence relations that come up in the analysis of randomized algorithms. The recurrence form is slightly different to the way you phrase it: rather than the coefficients of the recurrence being random, it's the "jump" itself that can be random. For example, a protoptypical example would be 
$T(n) = T(H(n)) + f(n)$, 
where H(n) is a random function of n (i.e a random variable that takes n as input and returns some random number less than n), and f(n) is some (deterministic) function. 
Richard Karp first studied these recurrences in a classic paper, and there was later followup work by Chaudhari and Dubhashi.
A: this is a Markov chain, so a lot can be said: ergodicity, CLT, invariance principles, etc... do you have a particular example in mind ?
A: If you are really interested in random linear recurrences you're in the realm of products of random matrices.  There's a lot been done in that field (look it up in math reviews), but you can start with the paper of Furstenberg and Kifer:
Random matrix products and measures on projective spaces
Israel Journal of Mathematics, Volume 46, Numbers 1-2 / June, 1983, pp 12-32
