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.