On the Kesten–Goldie constant

References

• G. Alsmeyer, On the stationary tail index of iterated random Lipschitz functions, Stochastic Process. Appl. 126 (2016), pp. 209–233.
   Web of Science ®Google Scholar
• G. Alsmeyer and S. Mentemeier, Tail behavior of sationary solutions of random difference equations: The case of regular matrices, J. Differ. Equ. Appl. 18(8) (2012), pp. 1305–1332.
   Web of Science ®Google Scholar
• L. Arnold and H. Crauel, Iterated function systems and multiplicative ergodic theory, in Diffusion Theory and Related Problems in Analysis II, M. Pinsky and V. Wihstatz, eds. Birkhauser, Boston, 1992, pp. 283–305.
   Google Scholar
• M. Babillot, P. Bougerol, and L. Elie, The random difference equation Xx=AnXn-1+Bn in the critical case, Ann. Probab. 25(1) (1997), pp. 478–493.
   Web of Science ®Google Scholar
• K. Bartkiewicz, A. Jakubowski, T. Mikosch, and O. Wintenberger, Stable limits for sums of dependent infinite variance random varibles, Prob. Theory Relat. Fields 150 (2011), pp. 337–372.
   Web of Science ®Google Scholar
• S. Brofferio and D. Buraczewski, On unbounded invariant measures of stochastic dynamical systems, Ann. Probab. 43 (2015), pp. 1456–1492.
   Web of Science ®Google Scholar
• D. Buraczewski and E. Damek, A simple proof of heavy tail estimates for affine type Lipschitz recursions, preprint (2016), to appear Stochastic Process. Appl.
   Google Scholar
• D. Buraczewski, E. Damek, Y. Guivarch, A. Hulanicki, and R. Urban, Tail-homogeneity of stationary measures for some multidimensional stochastic recursions, Probab. Theory Relat. Fields 145(3) (2009), pp. 385–420.
   Web of Science ®Google Scholar
• D. Buraczewski, E. Damek, and T. Mikosch, Stochastic Models with Power-law Tails. The Equation X=_dAX+B, Springer Series in Operations Research and Financial Engineering, Springer International Publishing, Basel, 2016.
   Google Scholar
• D. Buraczewski, E. Damek, and M. Mirek, Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems, Stochastic Process. Appl. 122 (2012), pp. 42–67.
   Web of Science ®Google Scholar
• B. Chauvin, Q. Liu, and N. Pouyanne, Limit distributions for multitype branching processes of m-ary search trees, Ann. Inst. Henri Poincare Probab. Stat. 50 (2014), pp. 628–654.
   Web of Science ®Google Scholar
• J.F. Collamore and A.N. Vidyashankar, Tail estimates for stochastic fixed point equations via nonlinear renewal theory, Stochastic Process. Appl. 123(9) (2013), pp. 3378–3429.
   Web of Science ®Google Scholar
• J.F. Collamore, G. Diao, and A.N. Vidyashankar, Rare event simulation for processes generated via stochastic fixed point equations, Ann. Appl. Probab. 24(5) (2014), pp. 2143–2175.
   Web of Science ®Google Scholar
• P. Diaconis and D. Freedman, Iterated random functions, SIAM Rev. 41(1) (1999), pp. 45–76.
   Web of Science ®Google Scholar
• M.Duflo, Random Iterative Systems, Springer Verlag, New York, 1997.
   Google Scholar
• J.H. Elton, A multiplicative ergodic theorem for Lipschitz maps, Stochastic Process. Appl. 34 (1990), pp. 39–47.
   Web of Science ®Google Scholar
• N. Enriquez, C. Sabot, and O. Zindy, A probabilistic representation of constants in Kesten’s renewal theorem, Probab. Theory Relat. Fields 144(3–4) (2009), pp. 581–613.
   Web of Science ®Google Scholar
• H. Furstenberg and H. Kesten, Products of random matrices Ann, Math. Statist. 31 (1960), pp. 457–469.
   Google Scholar
• C.M. Goldie, Implicit renewal theory and tails of solutions of random equations, Ann. Appl. Probab. 1(1) (1991), pp. 126–166.
   Google Scholar
• A.K. Grincevicius, On limit distribution for a random walk on the line, Lithuanian Math. J. 15 (1975), pp. 580–589. English translation.
   Google Scholar
• Y. Guivarc’h and E. Le Page, Spectral gap properties for linear random walks and Pareto’s asymptotics for affine stochastic recursions, Ann. Inst. Henri Poincaré Probab. Stat. 52 (2016), pp. 503–574.
   Web of Science ®Google Scholar
• Y. Guivarc’h and E. Le Page, On the homogeneity at infinity of the stationary probability for an affine random walk, Contemp. Math. 631 (2015), pp. 119–130.
   Google Scholar
• H. Hennion and L. Hervé, Central limit theorems for iterated random Lipschitz mappings, Ann. Probab. 32(3A) (2004), pp. 1934–1984.
   Web of Science ®Google Scholar
• H. Kesten, Random difference equations and renewal theory for products of random matrices, Acta Math. 131(1) (1973), pp. 207–248.
   Web of Science ®Google Scholar
• C. Klüppelberg and S. Pergamenchtchikov, The tail of the stationary distribution of a random coefficient AR(q) model, Ann. Appl. Probab. 14 (2004), pp. 971–1005.
   Web of Science ®Google Scholar
• M. Meiners and S. Mentemeier, Solutions to complex smoothing equations, preprint (2016), to appear in Probab. Theory Relat. Fields.
   PubMedGoogle Scholar
• M. Mirek, Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps, Probab. Theory Relat. Fields 151(3–4) (2011), pp. 705–734.
   Web of Science ®Google Scholar
• S.T. Rachev and G. Samorodnitsky, Limit laws for a stochastic process and random recursion arising in probabilistic modelling, Adv. Appl. Probab. 27(1) (1995), pp. 185–202.
   Web of Science ®Google Scholar
• W. Vervaat, On a stochastic difference equation and a representation of non-negative infinitely divisible random variables, Adv. Appl. Prob. 11 (1979), pp. 750–783.
   Web of Science ®Google Scholar