Stochastic Fixed Points and Nonlinear Perron-Frobenius Theorem

Article, Preprint English OPEN
Babaei Khezerloo, Esmaeil; Evstigneev, Igor; Pirogov, S. A.;
(2016)
  • Related identifiers: doi: 10.1090/proc/14075
  • Subject: Hilbert-Birkho metric | Stochastic equations | Random dynamical systems | andom monotone mappings | 37H10, 37H99, 37H15 | Contraction mappings | Mathematics - Dynamical Systems | Perron-Frobenius theory | nonlinear cocycles

We provide conditions for the existence of measurable solutions to the equation $\xi(T\omega)=f(\omega,\xi(\omega))$, where $T:\Omega \rightarrow\Omega$ is an automorphism of the probability space $\Omega$ and $f(\omega,\cdot)$ is a strictly non-expansive mapping. We us... View more
  • References (36)
    36 references, page 1 of 4

    [1] Arnold L., Random dynamical systems. Springer, Berlin (1998).

    [2] Arnold L., Gundlach V.M. and Demetrius L., Evolutionary formalism for products of positive random matrices. Ann. Appl. Prob. 4, 859-901 (1994).

    [3] Arnold L, Evstigneev I.V. and Gundlach V.M., Convex-valued random dynamical systems: A variational principle for equilibrium states. Random Oper. Stoc. Eqs. 7, 23-38 (1999).

    [4] Birkhoff G., Extensions of Jentzsch's theorem. Trans. Amer. Math. Soc. 84, 219-227 (1957).

    [5] Castaing C. and Valadier M., Convex analysis and measurable Multifunctions. Lecture Notes in Mathematics, No 580, Springer-Verlag, Berlin, Heidelberg, New York (1977).

    [6] Dellacherie C. and Meyer P.-A., Probabilities and Potential. North Holland, Amsterdam (1978).

    [7] Dempster M.A.H., Evstigneev I.V. and Schenk-Hopp´e K.R., Exponential growth of fixed-mix strategies in stationary asset markets. Finance Stoc. 7, 263-276 (2003).

    [8] Dempster M.A.H., Evstigneev I.V. and Taksar M.I., Asset pricing and hedging in financial markets with transaction costs: An approach based on the von Neumann-Gale model. Annals of Finance 2, 327-355 (2006).

    [9] Dobrushin R.L., Central limit theorem for nonstationary Markov chains, I and II. Theory Prob. Appl. 1, 65-80, 329-383 (1956).

    [10] Eisenack G. and Fenske C., Fixpunkttheorie. BI-Wissenschaftsverlag, Mannheim (1978).

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