Solutions of Backward Stochastic Differential Equations on Markov Chains
نویسندگان
چکیده
Consider a continuous time, finite state Markov chain X = {Xt, t ∈ [0, T ]}. We identify the states of this process with the unit vectors ei in R N , where N is the number of states of the chain. We consider stochastic processes defined on the filtered probability space (Ω, F , {Ft}, P), where {Ft} is the completed natural filtration generated by the σ-fields Ft = σ({Xu, u ≤ t}, F ∈ FT : P(F ) = 0), and F = FT . Note that, as X is right-continuous, this filtration is right-continuous. If At denotes the rate matrix for X at time t, then this chain has the representation
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