Lopes, João DiasCosta, Martim Roberto Alves da2024-01-092024-01-092023-12Costa, Martim Roberto Alves da (2023). “Products of i.i.d. random matrices and a theorem by Furstenberg”. Dissertação de Mestrado. Universidade de Lisboa. Instituto Superior de Economia e Gestãohttp://hdl.handle.net/10400.5/29743Mestrado Bolonha em Mathematical FinanceWe study the Lyapunov exponents associated to the product of i.i.d. random matrices linear cocyle in SL±(2,R). The existence of these quantities and conditions to guarantee strict positivity are established. These results are used to prove the exponential growth of a random Fibonacci sequence.engmaster thesis