- 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, Ann. Probab. 42 (2014), 649-688.
- 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.,26 (2013), 489-513.
- Nonconventional limit theorems in averaging, Annales de l'Institut H. Poincare, Probab. Stat. 50 (2014), 236-255.
- Nonconventional Poisson Limit Theorems, Israel J. Math., 195 (2013), 373-392.
- (with Y. Iron) Error estimates for binomial approximations of game put options, ISRN Probab. and Stat., volume 2014.
- (with S.R.S. Varadhan) Nonconventional large deviations theorems, Probab. Th. Related Fields,158(2014), 197-224.
- Hedging of game options in discrete markets with transaction costs, Stochastics 85 (2013), 667-681.
- Dynkin games and Israeli options, ISRN Probability and Statist., vol.2013
- Strong approximations for nonconventional sums and almost sure limit theorems, Stoch. Proc. Appl. 123 (2013), 2286-2302.
- (with A. Rapaport) Poisson and compound Poisson approximations in conventional and nonconventional setups, Probab. Th. Related Fields, 160(2014), 797-831.
- Lectures on large deviations in probability and dynamical systems, Proc. Symp. Pure Math. 89(2015), AMS, Providence, p.p.45-80.
- An Erd\" os-R\' enyi law for nonconventional sums, Electron. Commun. Probab. 20 (2015), no.83, 1-8.
- (with Y. Hafouta) A nonconventional local limit theorem, J. Theoret. Probab. 29 (2016), 1524-1553.
- (with Y. Dolinsky) Risk minimization for game options in markets imposing minimal transaction costs, Advances Appl. Probab., 48 (2016), 926--946.
- (with Y. Hafouta) Berry-Esseen type estimates for nonconventional sums, Stoch. Proc. Appl. 126 (2016), 2430-2464.
- (with Y. Hafouta) Nonconventional polynomial CLT, Stochastics 89 (2017), 550-591.
- (with S.R.S. Varadhan) Tails of polynomials of random variables and stable limits for nonconventional sums, J. Stat. Phys. 166 (2017), 575-608.
- Functional Erd\" os-R\' enyi law of large numbers for nonconventional sums under weak dependence, Elect. J. Probab. 22 (2017), no.23, 1-17.
- Erd\" os-R\' enyi law of large numbers in the averaging setup, Stoch. Dynam. 18 (2018), 1850018.
- Ergodic theorems for nonconventional arrays and an extension of the Szemer\' edi theorem, Discr. Cont. Dyn. Sys. 38 (2018), 2687--2716.
- (with Y.Hafouta, book) Nonconventional Limit Theorems and Random Dynamics, World Scientific, Singapore, 2018.
- (with A.Rapaport) Geometric law for multiple returns until a hazard, Nonlinearity, 32(2019), 1525--1545.
- (with S.Sodin) Nonconventional random matrix products, Elect. Comm. Probab. 23 (2018) .
- (book) Lectures on Mathematical Finance and Related Topics, World Scientific, Singapore, 2020.
- The strong Borel-Cantelli property in conventional and nonconventional setups, (in: Thermodynamic Formalism, M.Pollicott and S.Vaienti eds.), Lecture Notes in Math. 2290, Springer 2021.
- Limit theorems for numbers of multiple returns in nonconventional arrays, Ergod. Theory\&Dynam. Sys. 41(2021)
- Error estimates for discrete approximations of game options with multivariate diffusion asset prices, J. Stoch. Analysis, 2021.
- (with Fan Yang) Geometric law for numbers of returns until a hasard under $\phi$-mixing, Israel J. Math. (2021)
- (with D.Camargo and O.Zeitouni), The Erd\" os-R\' enyi-Shepp law of large numbers for ballistic random walk in random environment, Ann. l'Inst. H.Poincar\' e (B), Probab. Statist., (2021)
- Strong diffusion approximation in averaging and value computation in Dynkin's games, Ann. Appl. Probab., to appear.
- Strong diffusion approximation in averaging with dynamical systems fast motions, Israel J. Math. 251 (2022).
- (with P.Friz) Almost sure diffusion approximation in averaging via rough paths theory, arXiv:2111.05390.
- Some strong limit theorems in averaging, arXiv: 2209.10364
- Limit theorems for signatures, arXiv: 2306.13376
- Almost sure approximations and laws of iterated logarithm for signatures, arXiv: 2310.02665
- Almost sure diffusion approximation in averaging: direct proofs with rough paths flavors, arXiv: 2401.05038
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