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[JS03]<br />

Jean, J. and A.N. Shiryaev. (2003). Limit Theorems for Stochastic Processes, 2nd ed. Springer-Verlag, New<br />

York.<br />

[Kal97] Kallenberg, O. (1997). Foundations of Modern Probability. Springer-Verlag, New York.<br />

[KP99] Kloeden, P.E., and Platen, E. (1999). Numeri<strong>ca</strong>l Solution of Stochastic Differential Equations, Applied<br />

Mathematics, 23, Third corrected printing, Springer, New York.<br />

[MPS11] Mattingly, J.C., Pillai, N.S., and Stuart, A.M. (2011). Diffusion Limits of Random Walk Metropolis<br />

Algorithm in High Dimensions. Annals of Applied Probability, to appear.<br />

[MRR+53] Metropolis, N, Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of<br />

state <strong>ca</strong>lculations by fast computing machines. The Journal of Chemi<strong>ca</strong>l Physics, 21(6): 1087.<br />

[MT09] Meyn, S., and Tweedie., R.L. (2009). Markov Chains and Stochastic Stability, Second Edition. Cambridge<br />

University Press, NY.<br />

[NR05] Neal, P., and Roberts, G.O. (2006). Optimal S<strong>ca</strong>ling for Partially Updating MCMC Algorithms. Annals of<br />

Applied Probability. 16(2), 475-515.<br />

[NRY05] Neal, P., Roberts, G.O., and Yuen, W.K. (2007). Optimal S<strong>ca</strong>ling of Random Walk Metropolis Algorithms<br />

with Discontinuous Target Densities. Under revision for Annals of Applied Probability.<br />

[PST11] Pillai, N.S., Stuart A.M., and Thiéry (2011). Optimal S<strong>ca</strong>ling and Diffusion Limits for the Langevin<br />

Algorithm in High Dimensions. Submitted to the Annals of Statistics.<br />

[PG10] Pasari<strong>ca</strong>, C. and Gelman, A. (2010). Adaptively S<strong>ca</strong>ling the Metropolis Algorithm Using Expected Squared<br />

Jumping Distance. Statisti<strong>ca</strong> Sini<strong>ca</strong>, 20, 343-364.<br />

[RC04] Robert, C. and Casella, G. (2004) Monte Carlo Statisti<strong>ca</strong>l Methods, Second Edition. Springer, NY.<br />

[RGG97] Roberts, G.O., Gelman, A., Gilks, W.R. (1997). Weak Convergence and Optimal S<strong>ca</strong>ling of Random Walk<br />

Metropolis Algorithms. Ann. Appl. Probab. 7, 110-20.<br />

[RR98] Roberts, G.O., Rosenthal, J.S. (1998). Optimal S<strong>ca</strong>ling of Discrete Approximations to Langevin Diffusions.<br />

J.R. Stat. Soc. Ser. B Stat. Methodol. 60, 255-268.<br />

[RR01] Roberts, G.O., Rosenthal, J.S. (2001). Optimal S<strong>ca</strong>ling for various Metropolis-Hastings algorithms. Statis.<br />

Sci. 16, 351-67.<br />

[RR04] Roberts, G.O., Rosenthal, J.S. (2004). General State Space Markov Chains and MCMC Algorithms. Probab.<br />

Surveys 1, 20-71.<br />

[RT96] Roberts, G.O. and Tweedie, R.L. (1996). Exponential Convergence of Langevin Distributions and Their<br />

Discrete Approximations. Bernoull, 2(4), 341-363.<br />

[Ros08a] Rosenthal, J.S. (2008). Optimising Monte Carlo Search Strategies for Automated Pattern Detection.<br />

[Ros08b] Rosenthal, J.S. (2008). Optimal Proposal Distributions and Adaptive MCMC. Prepared for MCMC Handbook.<br />

[Ros10] Rosenthal, J.S. (2010). Optimal Proposal Distributions and Adaptive MCMC. Handbook of Markov Chain<br />

Monte Carlo, S. Brooks, A. Gelman, G. Jones, and X.-L. Meng (editors), Chapman & Hall / CRC Press.<br />

[SS05]<br />

Shakarchi, R. and Stein, E.M. (2005). Real Analysis - Measure Theory, Integration and Hilbert Spaces,<br />

Princeton University Press, Princeton.<br />

[SK11] Shalizi, C.R. with Aryeh Kontorovich. (2011) Almost None of the Theory of Stochastic Processes,<br />

Unpublished Manuscript. Available online http://www.stat.cmu.edu/~cshalizi/almost-none/v0.1.1/<br />

almost-none.pdf<br />

[Stro11] Stroock, D. (2011). Probability Theory - An Analytic View, Second Edition. Cambridge University Press,<br />

New York.<br />

[Tie94] Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Annals of Statistics.<br />

22, 1701-1762.<br />

50

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