Heavy tail properties of stationary solutions of multidimensional stochastic recursions
Guivarc'h, Yves
Original · EN
We consider the following recurrence relation with random i.i.d. coefficients (aₙ,bₙ): xₙ₊₁=aₙ₊₁ xₙ+bₙ₊₁ where aₙ∈ GL(d,R),bₙ∈ Rᵈ. Under natural conditions on (aₙ,bₙ) this equation has a unique stationary solution, and its support is non-compact. We show that, in general, its law has a heavy tail behavior and we study the corresponding directions. This provides a natural construction of laws with heavy tails in great generality. Our main result extends to the general case the results previously obtained by H. Kesten in [16] under positivity or density assumptions, and the results recently developed in [17] in a special framework.
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