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a jump process controlled by $X:$ $\\Pr(I_{t+s} = j | (X_u, I_u)_{u \\leq t}) = a_{i j}(X_t) s + o(s)$ for $i \\neq j$ on $\\{I_t = i \\}.$\n  We show that the behavior of $(X,I)$ is mainly determined by the behavior of the linearized process $(Y,J)$ where $\\dot{Y}_t = A^{J_t} Y_t,$ $A^i$ is the Jacobian 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