Publications

Funding sources from NSF provided under the grants DMS-0806145 / 0902075, CAREER award CMMI-0846816 and CMMI-1069064 are gratefully acknowledged. Previous support includes NSF grant 0595595

 

Recurrent theme in many of the following articles: Interplay between probability theory and optimal design of algorithms. In other words, what coarse analysis (typically done to obtain asymptotics) tells you about the design of efficient Monte Carlo simulation methods.

 

Publications and Scholarly Works (in cronological order within sections)

      Articles in Journals (published or accepted for publication)

      Articles in Journals (accepted up to minor revision or in their second round)

      Conference Proceedings (published or accepted for publication)

      Conference Proceedings (accepted up to a minor revision)

      Book Chapters and Encyclopedia Articles

      Editorials

      Articles Submitted for Publication (or to be submitted within the summer of 2011)

      Sample Pre-prints, Extended Abstracts and Working Papers (Please Request if Needed)

 

1.        Doctoral thesis title

 

Limit Theorems and Approximations with Applications to Insurance Risk and Queueing Theory (2004) Stanford University, Department of Management Science and Engineering. Advisor, Professor Peter Glynn

 

2.        Articles in Journals (published or accepted for publication)

      **   Denotes a publication given the 2009 Applied Probability Society Best Publication Award.

      *     Finalist paper in the 2010 INFORMS Junior Faculty Interest Group Forum Competition.

      &    Honorable mention in the 2011 INFORMS Nicholson Student Paper Competition (as supervisor).   

      %    Finalist INFORMS 2010 Junior Faculty Interest Group competition.

      Most links of the published or accepted papers prompt to a summary page which includes a bibtex record and the paper.

 

1.     Pekoz, E., and Blanchet, J.  Heavy-traffic Limit Theorems via Embeddings. Probability in the Engineering and Informational Sciences, 20 (2006), pp. 595-598

2.     Blanchet, J., and Glynn, P.  Corrected Diffusion Approximations for the Maximum of Light-tailed Random Walk. Annals of Applied Probability, 16 (2006), 2, pp. 952-983. (T)

3.     Blanchet, J., and Glynn, P. Uniform Renewal Theory with Applications to Geometric Sums. Advances in Applied Probability, 39 (2007), 4, pp 1070 – 1097.

4.     Blanchet, J., Glynn, P., and Liu, J. C. Fluid Heuristics, Lyapunov Bounds and Efficient Importance Sampling for a Heavy-tailed G/G/1 Queue. Queueing Systems: Theory and Applications, 56 (2007), 3, pp. 99 – 113.** (S)

5.     Blanchet, J. and Glynn, P. Efficient Rare Event Simulation for the Single Server Queue with Heavy Tailed Distributions.  Annals of Applied Probability, 18 (2008), 4, pp. 1351 – 1378.**

6.     Blanchet, J., and Liu, J. C. State-dependent Importance Sampling for Regularly Varying Random Walks. Advances in Applied Probability, 40, (2008), pp 1104-1128. (S)

7.     Asmussen, S., Blanchet, J., Rojas-Nandayapa, L., and Juneja, S. Efficient Simulation of Tails Probabilities of Sums of Correlated Lognormals. To appear in Annals of Operations Research, Special vol. in honor of Reuven Rubinstein.

8.     Blanchet, J., Glynn, P., and Lam, H. Rare-event Simulation of a Slotted Time M/G/s Queue. Queueing Systems: Theory and Applications, 67, (2009), pp 33 – 57. (S), (I)

9.     Olvera-Cravioto, M., Blanchet, J. and Glynn P. On the Transition from Heavy Traffic to Heavy Tails for the M/G/1 Queue I:  The Regularly Varying Case. Annals of Applied Probability, 21, (2011), pp 645-668. (C)

10.  Blanchet, J. Importance Sampling and Efficient Counting for Binary Contingency Tables. Annals of Applied Probability, 19, (2009),  pp 949 – 982.**

11.  Blanchet, J., and Li, C. Efficient Rare-event Simulation for Heavy-tailed Compound Sums. ACM TOMACS Transactions in Modeling and Computer Simulation, 21, (2011), pp 1-10.

12.  Blanchet, J., and Li, C. Efficient Simulation for the Maximum of Infinite Horizon Gaussian Processes. To appear in Journal of Applied Probability. (S)

13.  Blanchet, J. and Liu, J. Efficient Importance Sampling in Ruin Problems for Multidimensional Regularly Varying Random Walks. Journal of Applied Probability, 47, (2010), 301-322.* (S)

14.  Blanchet, J. and Zwart, B. Asymptotic Expansions of Renewal Equations with Applications to Insurance and Processor Sharing. Math. Meth. in Oper. Res., 72, (2010), 311-326.

15.  L'Ecuyer, P.,  Blanchet, J., Tuffin, B., and Glynn, P. W.  Asymptotic Robustness of Estimators in Rare-Event Simulation. ACM TOMACS Transactions in Modeling and Computer Simulation, 20, (2010), pp 1-41.

16.  Lam, H. K., Blanchet, J., Bazant, M., and Burch, D. Corrections to the Central Limit Theorem for Heavy-tailed Probability Densities. To appear in Journal of Theoretical Probability. (Available through on-line first since September 17, 2011.)  (S)

17.  Blanchet, J., Leder, K., Shi, Y. Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson Networks. Stochastic Systems, 1, (2011), pp 306-339. (P, S)

18.  Blanchet, J., and Rojas-Nandayapa, L. Efficient Simulation of Tail Probabilities of Sums of Dependent Random Variables. Journal of Applied Probability, Special Vol. 48A, (2011), 147-165.

19.  Blanchet, J., and Sigman, K. On Exact Sampling of Stochastic Perpetuities. Journal of Applied Probability, Special Vol. 48A, (2011), 165-183. (C)

20.  Blanchet, J., and Lam, H. State-dependent Importance Sampling for Rare Event Simulation: An Overview and Recent advances. Surveys in Operations Research and Management Sciences, 17, (2012), 38-59 (S)

21.  Adler, R., Blanchet, J., and Liu, J. C. Efficient Simulation of High Excursions of Gaussian Random Fields. Annals of Applied Probability, 22, (2012), 1167-1214. (S)

22.  Blanchet, J. and Pacheco-Gonzales, C. Uniform Convergence to a Law Containing Gaussian and Cauchy Distributions. Probability in the Engineering and Informational Sciences, 26, (2012), 437-448

23.  Blanchet, J., and Stauffer, A. Characterizing Optimal Sampling of Binary Contingency Tables via the Configuration Model. Random Structures and Algorithms, 42, 159-184 (2012). (See also http://arxiv.org/abs/1007.1214.)

24.  Blanchet, J., Glynn, P., and Leder, K. On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling. ACM TOMACS Transactions in Modeling and Computer Simulation, 22, (2012). Article No. 13.

25.  Blanchet, J., Lam, H., and Zwart, B. Efficient Rare Event Simulation for Perpetuities. Stochastic Processes and their Applications, 122, (2012), 3361-3392. (S)

26.  Blanchet, J. Optimal Sampling of Overflow Paths in Jackson Networks.  Mathematics of Operations Research, 38, (2013), 698-719.

27.  Blanchet, J., and Liu, J. C. Efficient Simulation and Conditional Functional Limit Theorems for Ruinous Heavy-tailed Random Walks. Stochastic Processes and their Applications, 122, (2012), 2994-3031. (S)

28.  Blanchet, J. and Shi, Y. Strongly Efficient Algorithms via Cross Entropy for Heavy- tailed Systems. Operations Research Letters, 41, (2013), 271-276. (S)

29.  Blanchet, J., and Liu, J. C. Total Variation Approximations for Multivariate Regularly Varying Random Walks Conditioned on Ruin. To appear in Bernoulli. (S) http://www.e-publications.org/ims/submission/index.php/BEJ/user/submissionFile/10999?confirm=27b27289 %

30.  Blanchet, J., Glynn, P., and Meyn, S. Large Deviations for the Empirical Mean of an M/M/1 Queue. Submitted to Queueing Systems: Theory and Applications, 73, (2013), 425-446.

31.  Blanchet, J. and Lam, H. A Heavy Traffic Approach to Modeling Large Life Insurance Portfolios. Insurance: Mathematics and Economics, 53, (2013), 237-251. (S)

32.  Blanchet, J. and Mandjes, M. Asymptotics of the Area under the Graph of a Lévy-driven Workload Process. Accepted in Operations Research Letters, 41, (2013), 730-736.

33.  Blanchet, J., Hult, H., and Leder, K. Rare-event simulation for stochastic recurrence equations with heavy-tailed innovations. ACM TOMACS Transactions on Modeling and Computer Simulations. (Supplement), 23, (2013), Article No. 22.

34.  Blanchet, J., and Lam, H. Rare-event Simulation for Many Server Queues. To appear in Mathematics of Operations Research. (S)

35.  Blanchet, J., Chen, X., and Lam, H. Two-parameter Sample Path Large Deviations for Infinite Server Queues. To appear in Stochastic Systems.

36.  Blanchet, J. and Lam, H. Uniform Large Deviations for Heavy-Tailed Queues under Heavy-Traffic. Bulletin of the Mexican Mathematical Society, Bol. Soc. Mat. Mexicana (3) Vol. 19, 2013 Special Issue for the International Year of Statistics.

 

3.        Articles in Journals (accepted up to minor revision)

37.  Blanchet, J. and Chen, X. Steady-state Simulation for Reflected Brownian Motion and Related Networks. Accepted up to minor revisions in Annals of Applied Probability. (S)

38.  Blanchet, J., Gallego, G. and Goyal, V. A Markov Chain Approximation to Choice Modeling. Submitted to Operations Research.

39.  Blanchet, J. and Wallwater, A. Exact Sampling for the Steady-state Waiting Time of a Heavy-tailed Single Server Queue.

 

4.        Conference Proceedings (published or accepted for publication)

Note:  + represents a paper for which there is journal version listed above, otherwise there is no overlap in content with papers that have appeared in journals.

 

40.  Blanchet, J., and Glynn, P. Strongly-efficient Estimators for Light-tailed Sums. ACM: Proc Valuetools’06, Article 18,  (2006). (S)

41.  Blanchet, J., Liu, J. C. and Glynn, P. Importance Sampling and Large Deviations. Proc. Valuetools’06, Article 20,  (2006). (S)

42.  Blanchet, J., and Liu, J. C. Efficient Simulation of Large Deviation Probabilities for Sums of Heavy-tailed Increments. Proc. Winter Simulation Conference (2006), pp. 757-764. (S) +

43.  Blanchet, J., and Zwart, B.  Importance Sampling of Compounding Processes. Proc. Winter Simulation Conference (2007), pp. 372-379. (I) +

44.  Blanchet, J., and Liu, J. C.  Rare-event Simulation of Multidimensional Random Walks with t-distributed Increments. Proc. Winter Simulation Conference (2007), pp. 395-402. (S) (I) +

45.  Blanchet, J., and Liu, J. C. Path-sampling for State-dependent Importance Sampling. Proc. Winter Simulation Conference (2007), pp. 380-388.  (S) (I)

46.  Zhang, X., Blanchet, J., and Glynn, P. Efficient Suboptimal Rare-event Simulation. Proc. Winter Simulation Conference (2007), pp. 389-394. (I)

47.  Blanchet, J., Rojas-Nandayapa, L., and Juneja, S. Fast Simulation of Sums of Correlated Lognormals. Proc. Winter Simulation Conference (2008), pp. 607-614. +

48.  Adler, R., Blanchet, J. and Liu, J. C. Efficient Simulation for Tail Probabilities of Gaussian Random Fields. Proc. Winter Simulation Conference (2008), pp 328-336. (S) (I) +

49.  Blanchet, J., Liu, J. C., and Zwart, B. A Large Deviations Perspective to Ordinal Optimization of Heavy-tailed Systems. Proc. Winter Simulation Conference (2008), pp. 489-494. (S) (I)

50.  Blanchet, J., Leder, K. and Glynn, P. Efficient Simulation for Light-tailed Sums: An Old Folk Song Sung to a Faster New Tune. Springer volume for MCQMC 2008 edited by Pierre L’Ecuyer and Art Owen. (2009), pp. 227-248. (P)

51.  Blanchet, J., and Glynn, P. Efficient Rare Event Simulation of Continuous Time Markovian Perpetuities. Proc. Of the Winter Simulation Conference (2009), pp. 444-451. (I)

52.  Zhang, X., Glynn, P., Giesecke, K., Blanchet, J. Rare Event Simulation of a Generalized Hawkes Process. Proc. Of the Winter Simulation Conference (2009), pp. 1291-1298. (I)

53.  Blanchet, J., Liu, J. C., and Xang, X. Monte Carlo for Large Credit Portfolios with Potentially High Correlations. Proc. of the Winter Simulation Conference (2010), pp. 328-336. (S) (I)

54.  Blanchet, J., and Lam, H. Rare Event Simulation Techniques. Proc.  Winter Simulation Conference (2011). (S) (I)

55.  Blanchet, J., and Shi, Y. Strongly Efficient Cross Entropy Method for Heavy-tailed Simulation, Winter Simulation Conference (2011). (S) (I)

56.  Blanchet, J., Li, Juan, and Nakayama, M. A Conditional Monte Carlo for Estimating the Failure Probability of a Network with Random Demands (2011). (S) (I)

57.  Blanchet, J., Hult, H., and Leder, K. Efficient Importance Sampling for Affine Regularly Varying Markov Chains (2011).

58.  Blanchet, J., and Lam, H. Importance Sampling for Actuarial Cost Analysis under a Heavy Traffic Model. Proc.  Winter Simulation Conference (2011). (S) (I)

59.  Blanchet, J., and Dong, J. Sampling point processes on stable unbounded regions and exact simulation of queues. Proc. Winter Simulation Conference (2012): 11 (S) (I)

60.  Blanchet, J., Glynn, P., and Zheng, S. Empirical Analysis of a Stochastic Approximation Approach for Computing Quasi-stationary Distributions. EVOLVE 2012: 19-37

61.  Blanchet, J., Gallego, G., and Goyal, G. A Markov chain approximation to choice modeling. ACM Conference on Electronic Commerce 2013: 103-104

62.  Blanchet, J. and Shi, Y. Efficient Rare Event Simulation via Particle Methods for Heavy-tailed Sums. Proc. Winter Simulation Conference (2013).

63.  Blanchet, J., Murthy, K., and Juneja, S. Optimal Rare Event Monte Carlo for Markov Modulated Regularly Varying Random Walks. Proc. Winter Simulation Conference (2013).

 

5.        Conference Proceedings (accepted up to a minor revision)

 

6.        Chapters in Books (published or accepted for publication)

 

64.  Blanchet, J., and Rudoy, D. Rare-event Simulation and Counting Problems. In Rare-event Estimation using Monte Carlo Methods, Rubino, G. and Tuffin, B. Eds. Wiley, 2009.

65.  Blanchet, J., and Mandjes, M. Rare-event Simulation for Queues. In Rare-event Estimation using Monte Carlo Methods, Rubino, G. and Tuffin, B. Eds. Wiley, 2009.

66.  Blanchet, J. and Pacheco-Gonzales C. Large Deviations and Applications to Quantitative Finance. Encyclopedia of Quantitative Finance, Edited by Rama Cont. Wiley 2009.

 

7.        Editorials

 

67.  Blanchet, J., and Mandjes, M. Rare-event Simulation for Queues (2007). Queueing Systems: Theory and Applications. Vol. 57 Numbers 2 and 3. Editorial.

68.  Blanchet, J., and Roberts, G. Simulation of Stochastic Networks and related topics (2012). Queueing Systems: Theory and Applications. Vo. 73 Numbers 4. Editorial.

 

8.        Journal Articles Submitted for Publication

69.  Blanchet, J. and Shi, Y. Modeling and Efficient Rare Event Simulation of Systemic Risk in Insurance-Reinsurance Networks. Under revision. (S)

70.  Blanchet, J. and Ruf, J. A Weak Convergence Criterion Constructing Changes of Measure. Under revision.

71.  Blanchet, J. and Dong, J. Exact Simulation of Loss Networks and Running Time Analysis in Heavy Traffic. Under revision.

72.  Blanchet, J., and Glynn, P.  Approximations for the Distribution of Perpetuities with Small Interest Rates. Submitted

73.  Murthy, K., Juneja, S., and Blanchet, J. State-independent Importance Sampling for Random Walks with Regularly Varying Increments. Submitted.

74.  Blanchet, J. and Dong, J. Rare-event Simulation for the Steady-state Queue Length Process of Many Server Queues. Submitted.

75.  Zhang, X., Blanchet, J., Giesecke, K., and Glynn, P. Affine Point Processes: Approximation and Efficient Simulation. Submitted.

 

9.        Some Preprints and Technical Reports. BEWARE the presentation requires polishing, but the math should be fine – however, I’d appreciate comments if you see any problem. Also, please, email me if you’re interested in any of the preprints below and is not uploaded.

 

75.  Blanchet, J., Liu, J. C., and Glynn, P. Efficient Rare Event Simulation for Regularly Varying Multi-server Queues. To be submitted to Queueing Systems Theory and Applications. Summary: This paper provides the first asymptotically optimal (in fact we show strong optimality) algorithm for estimating the tails of the steady-state delay in a multi-server queue with heavy-tailed increments. The technique is the one introduced in “Fluid Heuristics, Lyapunov Bounds and Efficient Importance Sampling for a Heavy-tailed G/G/1 Queue (with P. Glynn, and J. C. Liu), 2007. QUESTA, 57, 99-113”. The construction in the multidimensional case is interesting because of the way in which fluid heuristics need to adapt to accommodate the boundaries.

76.  Blanchet, J. and Glynn, P. Large Deviations and Sharp Asymptotics for Perpetuities with Small Discount Rates . Summary: This paper relates to Approximations for the Distribution of Perpetuities with Small Discount Rates (with P. Glynn). Instead of concentrating on the central limit theorem region we develop large deviations asymptotics. The paper contains characterizations of exponential tightness in a suitable (and useful for the analysis of perpetuities) class of topologies. It also develops exact tail asymptotics for discrete and continuous perpetuities and it shows qualitative differences arising from the discrete and continuous nature of perpetuities. I think this line of research is particularly interesting these days in which the interest rates are small.

77.  Blanchet, J. and Glynn, P. Corrected Diffusion Approximations for the Maximum of Random Walks with Heavy-tails (with P. Glynn). (Please, refer to Chapter 3 of my dissertation for more details). Summary: This paper continues the study of corrected diffusion approximations for first passage times of random walks with a small negative drift $mu$. The paper “Complete Corrected Diffusion Approximations for the Maximum of Random Walk (2006) Ann. of App. Prob., (with P. Glynn)” assumes finite exponential moments. Here we show that if one has $alpha + 2$ moments then one can add $alpha$ correction terms resulting in an approximation with an error of size o(mu^alpha).

78.  Blanchet, J., and Lam, H. K. Corrected Diffusion Approximations for Moments of the Steady-state Waiting Time in a G/G/1 Queue. Summary: This paper revisits Complete Corrected Diffusion Approximations for the Maximum of Random Walk (with P. Glynn), 2006. Ann. of App. Prob., 16, p. 951-953. We now concentrate on moments rather than the tail of the distribution. Recently Janssen and van Leeuwaarden (2007), Stoch. Proc. and their Appl., 117, 1928-1959, obtained complete asymptotic expansions for the Gaussian case. Here we obtain expansions for any strongly non-lattice distribution exponentially decaying tails.

79.  Blanchet, J., Glynn, P. and Zheng, J.. A Stochastic Approximations Algorithm for the Quasi-stationary Distribution of a Markov chain. Summary: This paper provides the analysis of a very nice algorithm that Peter Glynn told me about. He reports that he knew this from a faculty in the Biostatistics Department at Harvard. Here is how it goes. You wish to compute “lambda” > 0 and a probability vector “mu” such that mu*P = lambda*mu, where P is strictly sub-stochastic (and irreducible). So, you add a cemetery state to make P stochastic. At state k you have a current estimate mu(k,y) for mu(y) (“y” is any non-cemetery state of the chain) and lambda(k) for lambda. You start iteration k+1 by picking a point according to mu(k). Run the chain until it hits the cemetery state. Record the time tau(k+1) and the number of times, N(k+1,y), the chain visits state “y” in the k+1 iteration prior to absorption. Then, let lamda(k+1) = [k*lambda(k)+tau(k+1)]/(k+1) and mu(k+1,y)=[mu(k,y)*lambda(k)+N(k+1,y)]/lambda(k+1). The paper uses the ODE stochastic approximations method to prove the validity of the algorithm and analyze its rate of convergence.

80.  Blanchet, J., and Lam, H. K. Rare-event Simulation for Markov Modulated Heavy-tailed Random Walks. Summary: This paper considers rare-event simulation for first passage time probabilities of Markov modulated regularly varying random walks. We use the Lyapunov-bound technique to design the importance sampling estimator. What is interesting is that the Lyapunov bound, instead of being tested in one step of the underlying process, as we typically do, it must be tested after K steps (for K large enough) or at regeneration times of the underlying Markov modulation.

81.  Blanchet, J., and Meng, X. L. Exact Sampling, Regeneration and Minorization Conditions. Summary: This report builds on a paper by Asmussen, Glynn and Thorisson (1992) TOMACS. Here we note that if one has a Harris chain with regeneration time “tau” and if one can compute a constant C>0 such that E(tau^p)<=C for p>1 (or Eexp(delta*tau)<C) then one can generate exact samples from  the steady-state distribution of chain in question in finite time almost surely, provided that one can identify the regeneration times of the chain. Unfortunately, although the expected termination time will typically be infinite. HOWEVER! I recently figured out how to fix the problem for a large class of chains! So, I’ll get back to this problem soon!

 

Some work in Progress

82.  Blanchet, J. and Dupuis, P. Fast Simulation of Brownian Motion Avoiding Random Obstacles.

83.  Blanchet, J. and Kirkpatrick, K. Asymptotic Analysis of a Dynamic Quantum Curie-Weiss-type model.