Papers and Preprints (from 1990):

• A discrete time version of the Wentzell-Freidlin theory, Annals of Probability, 18(1990),1676-1692.
• Principal eigenvalues, topological pressure, and stochastic stability of equilibrium states, Israel J. Math., 70(1990),1-47.
• Large deviations in dynamical systems and stochastic processes, Transactions of the American Mathematical Society, 321(1990),505-524.
• A lower bound for Hausdorff dimension of harmonic measures on negatively curved manifolds, Israel J. Math.,71(1990),339-348.
• Random perturbations of dynamical systems:a new approach,Lectures in Applied Math.,27 (1991),163-173.
• (with S. Newhouse) A global volume lemma and applications, Israel J. Math.,74 (1991),209-223.
• Large deviations for random expanding maps, in: Lyapunov exponents (ed. L.Arnold, H.Crauel, J.-P.Eckmann) Lecture Notes in Math. 1486 (1991), 178-186.
• Principal eigenvalues and equilibrium states corresponding to weakly coupled parabolic systems of PDE, J.D'Analyse Mathematique 59(1992),89-102.
• Equilibrium states for random expanding transformations, Random and Computational Dynamics,1(1992), 1-31.
• Averaging in dynamical systems and large deviations,Inventiones mathematicae 110 (1992), 337-370.
• A variational approach to the random diffeomorphisms type perturbations of a hyperbolic diffeomorphism,in:Mathematical Physics X, p.334-340,ed.K.Schmudgen, Springer-Verlag,1992.
• (with M Brin) Harmonic measures on covers of Riemannian surfaces of nonpositive curvature,Trans.Amer.Math.Soc. 340(1993), 373-393.
• Topics on Large Deviations and Random Perturbations, Carolina Lecture Series, Univ.of North Carolina,Chapel Hill,1993.
• Large deviations,averaging,and periodic orbits of dynamical systems, Comm.Math.Phys. 162(1994), 33-46.
• (with A.Eizenberg and B.Weiss) Large deviations for $ Z^d$-actions, Comm.Math.Phys. 164 (1994), 433-454.
• Harmonic functions on Riemannian manifolds: a probabilistic approach, in: The Dynkin Festschrift, Markov processes and their Applications (ed. M.I.Freidlin), p.p.199-207, Birkhauser, Boston, 1994.
• Spectrum, harmonic functions,and hyperbolic metric spaces, Israel J. Math. 89 (1995), 377-428.
• (with M.Brin) Brownian motion and harmonic functions on polygonal complexes, in: Stochastic Analysis (ed. M.Cranston and M.Pinsky), AMS Proc. Symposia in Pure Math. 57 (1995), 227-237.
• Markov processes and harmonic functions on hyperbolic metric spaces, in: Stochastic Analysis (ed. M.Cranston and M.Pinsky),AMS Proc. Symposia in Pure Math. 57 (1995), 307-322.
• Limit theorems in averaging for dynamical systems, Ergod. Theory and Dynam. Sys. 15 (1995), 1143-1172.
• Multidimensional random subshifts of finite type and their large deviations, Prob. Theory and Relat. Fields 102 (1995), 223-248.
• Fractals via random iterated function systems and random geometric constructions, in: Fractal Geometry and Stochastics (ed. C.Bandt, S.Graf, and M.Zahle), Progress in Probability 37, Birkhauser, 1995.
• (with K.Khanin) Thermodynamic formalism for random transformations and statistical mechanics, in: Sinai's Moscow Seminar on Dynamical Systems (ed. L.A.Bunimovich, B.M.Gurevich, Ya.B.Pesin), Amer. Math. Soc. Translations 171 (1995), 107-140.
• Large deviations for paths and configurations counting, in: Ergodic Theory of $Z^d-$Actions (ed. M.Pollicott and K.Schmidt), London Math. Soc. Lecture Notes Series 228 (1996), 415-432.
• Fractal dimensions and random transformations, Trans. Amer. Math. Soc. 348 (1996), 2003-2038.
• Perron-Frobenius theorem, large deviations, and random perturbations in random environments, Math. Zeitschrift 222 (1996), 677-698.
• (with M.Cranston and W.S.Kendall) Gromov's hyperbolicity and Picard's little theorem for harmonic maps, in: Stochastic Analysis and Applications (Proceedings of the Fifth Gregynog Symposium 1995, ed. I.M.Davies, A.Truman, and K.D.Elworthy), p.p. 139-164, World Scientific, Singapore, 1996.
• (with H.Kunita) Random positive semigroups and their random infinitesimal generators, in: Stochastic Analysis and Applications (Proceedings of the Fifth Gregynog Symposium 1995, ed. I.M.Davies, A.Truman, and K.D.Elworthy), p.p. 270-285, World Scientific, Singapore, 1996.
• The Burgers equation with a random force and a general model for directed polymers in random environments, Prob. Theory and Relat. Fields 108 (1997), 29-65.
• Computations in dynamical systems via random perturbations, Discrete and Continuous Dyn. Sys. 3 (1997), 457--476.
• Limit theorems for random transformations and processes in random environments, Trans. Amer. Math. Soc. 350 (1998), 1481-1518.
• Random dynamics and its applications, Documenta Math. J. DMV, Extra Volume ICM 1998, vol. II, 809-818.
• (with V.M.Gundlach) Random hyperbolic systems, in: Stochastic Dynamics (H.Crauel and M.Gundlach eds.), Springer-Verlag, 1999, p.p. 117-145.
• (with V.M.Gundlach) Expansiveness, specification, and equilibrium states for random bundle transformations, Discrete and Continuous Dynam. Sys. 6 (2000), 89--120.
• Game options, Finance and Stochastics 4(2000), 443--463.
• On the topological pressure for random bundle transformations, in: Rohlin's memorial volume (V.Turaev and A.Vershik ed.), Amer. Math. Soc. Transl. (2) v.202 (2001), 197--214.
• (with M.Brin) Brownian motion, harmonic functions and hyperbolicity for Euclidean complexes, Math. Zeitschrift, 237 (2001), 421--468.
• "Random" random matrix products, J. D'Analise Math. 83 (2001), 41--88.
• (with N.Enriquez) Markov chains on graphs and Brownian motion, J. Theoretical Probab., 14 (2001), 495--510.
• Averaging and climate models, in: Stochastic Climate Models (ed. P.Imkeller and J. von Stroch ), Progress in Probability v.49, Birkh\" auser, Basel, 2001.
• Random $f$-expansions, Proc. Simposia in Pure Math., 69, p.p. 385--407, Amer. Math. Soc. (2001).
• (with Y.Peres and B.Weiss) A dimension gap for continued fractions with independent digits, Isr. J. Math. 124 (2001), 61--76.
• Stochastic versions of Anosov's and Neistadt's theorems on averaging, Stoch. and Dynam. 1 (2001), 1--21.
• (with B.Weiss) Generating partitions for random transformations, Ergodic Th.&Dyn. Sys, 22 (2002), 1--18.
• (with Eizenberg) Large deviations for probabilistic cellular automata, J. Stat. Phys. 108 (2002), 1255--1280.
• L^2 diffusion approximation for slow motion in averaging, Stoch. and Dynam. 3 (2003), 213--246.
• Averaging in difference equations driven by dynamical systems, Ast\' erisque 287 (2003), 103--123.
• Averaging principle for fully coupled dynamical systems and large deviations, Ergod. Th.&Dyn. Sys. 24 (2004), 847--871.
• (with V.Bakhtin) Diffusion approximation for slow motion in fully coupled averaging, Prob. Th. and Related Fields 129 (2004), 157--181.
• Some recent advances in averaging, in: Modern Dynamical Systems and Applications (M.Brin, B.Hasselblatt, Ya.Pesin eds.), Cambridge University Press, Cambridge 2004.
• (with A.Eizenberg) Large deviations for probabilistic cellular automata II, J. Stat. Phys. 117 (2004), 845--889.
• New directions in fully coupled averaging for dynamical systems, RIMS Kokyuroku 1404, Kyoto University, Kyoto (2004), 45--63.
• Another proof of the averaging principle for fully coupled dynamical systems with hyperbolic fast motions, Discrete and Cont. Dyn. Sys. 13 (2005), 1187--1201.
• (with P.-D.Liu) Random dynamics, in: Handbook of Dynamical Systems, vol. 1B (B.Hasselblatt and A.Katok--eds.),p.p.379--499, North-Holland/Elsevier, Amsterdam, 2006.
• Error estimates for binomial approximations of game options, Annals of Appl. Probab. 16 (2006),984--1033.
• Correction, Ann. Appl. Prob. 16 (2006), 2273--2275.
• (with Y.Dolinsky) Another correction ..., Annals of Appl. Probab., 18 (2008)
• (with Y.Dolinsky) Hedging with risk for game options in discrete time, Stochastics, 79 (2007), 169--195.
• Optimal stopping and strong approximation theorems, Stochastics, 79 (2007), 253--273.
• (with M.Denker and M.Stadlbauer) Conservativity of random Markov systems, Ergod. Th. and Dyn. Sys., 28 (2008), 67-85.
• Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging, Memoirs of Amer. Math. Soc. 944, AMS, Providence, 2009.
• Thermodynamic formalism for random countable Markov shifts, Disc. Cont. Dyn. Sys. 18 (2008), 1737-1770.
• (with V.Bakhtin) Nonconvergence examples in averaging, Contemporary Math., 469 (2008), 1-18.
• Thermodynamic formalism for random transformations revisited, Stochastics and Dynam., 8 (2008), 77-102.
• (with Y.Dolinsky) Binomial approximations of shortfall risk for game options, Ann. Appl. Probab., 18 (2008),1737-1770
• Convergence, nonconvergence and adiabatic behavior in fully coupled averaging, Nonlinearity 21 no.3 (2008), T27-T32.
• Nonconventional limit theorems, Probability Theory and Related Fields 148(2010), 71-106.
• (with Y.Dolinsky and Y.Iron) Perfect and partial hedging for game swing options in discrete time, Math. Finance 21(2011), 447-474
• (with Y.Iron) Hedging of swing game options in continuous time, Stochastics 83 (2011), 365-404
• A strong invariance principle for nonconventional sums, Probab. Theory and Rel. Fields 155 (2013), 163--186.

(with S.R.S.Varadhan) Nonconventional limit theorems in discrete and continuous time via martingales, Annals of Probab., to appear.

• A Nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets, Stochastics and Dynamics 12 (2012)

A Nonconventional invariance principle for random fields, J. Theoret. Probab., to appear

Nonconventional limit theorems in averaging, Annales de l'Institut H. Poincare, Probab. Stat., to appear.

Nonconventional Poisson Limit Theorems, Israel J. Math., to appear

• (with Y. Iron) Error estimates for binomial approximations of game put options, arXiv 1206.0153
• (with S.R.S. Varadhan) Nonconventional large deviations theorems, Probab. Th. Related Fields, to appear
• Hedging of game options in discrete markets with transaction costs, Stochastics, to appear