| MSU Statistics and Probability Faculty Publications |
| Shlomo Levental Publications |
1. Uniform Limit Theorems. Ph.D Thesis, University of Wisconsin-Madison,
August 1986.
2. Uniform Limit Theorems for Harris Recurrent Markov Chains. Theory of Probability and Related Topics, Vol 80, 101-118, 1988.
3. Proof of Liggett's Version of the Subadditive Erogodic Theorem. Proceedings of American Mathematical Society, Vol 102, 169-173, 1988.
4. A Uniform CLT for Uniformly Bounded Families of Martingale Differences. Journal of Theoretical Probability, Vol 2, 171-287, 1989.
5. On Pricing of Market-Indexed Certificates of Deposit. Statistics & Probability Letters, Vol 8, 329-334, 1989 (joint with J. Gardiner).
6. Weak Convergence in Explosive Autoregression. The Annals of Statistics, Vol 17, 1784- 1794, 1989 (joint with Hira Koul).
7. Uniform CLT for Markov Chains with Discrete State Space. Stochastics Processes and their Applications, Vol 30, 245-253, 1990.
8. Uniform CLT for Markov Chains and its Invariance Principle: A Martingale Approach.
Journal of Theoretical Probability, Vol 8, 549-570, 1995 (joint with J. Bae).
9. A Uniform CLT for Continuous Martingales. Journal of the Korean Statistical Society, Vol 24, 225-231, 1995 (joint with J. Bae).
10. Necessary and Sufficient Conditions for Absence of Arbitrage with Tame Portfolios. Annals of Applied Probability, Vol 5, 906-925, 1995 (joint with A.V. Skorokhod).
11. On the Possibility of Hedging options in the Presence of Transactions Costs. Annals of Applied Probability, 1997, Vol. 7, No. 2, 410-443. (Joint with A.V. Skorokhod).
12. Permutations, Signs and the Brownian Bridge. Statistics & Probability Letters, Vol. 46,
Issue 3, 270-276, 2000.
13. A maximal inequality for real numbers with application to exchangeable random
variables. Accepted for publication in Theory of Probability and its Applications, v 45, issue 3, pp 615-621, 2000.
14. On coupling of Brownian Bridges. Theory of Probability and its Applications, v 46, issue 1, pp 169-175, 2001.
15. The Super-Replication Problem via Probabilistic Methods. Annals of Applied Probability, 2003, Vol 13, No 2, 742 - 773. (joint with M. Ryznar).
16.Some problems in the theory of super-replication: Market viability and multidimensional options. Technical report 594, July 2000. (joint with M. Ryznar ).
17. On a.s. convergence of the quadratic variation of Brownian Motion. Stochastics Processes and their Applications, Vol 106, Issue 2, August 2003, Pages 317-333. (joint with R.V. Erickson).
18. Prokhorov blocks and strong law of large numbers under rearrangements (joint with S. Chobanyan and V. Mandrekar ). Journal of Theoretical Probability,
Vol 17, Issue 3, July 2004.
19. General Maximal Inequalities related to strong law of large numbers (joint with S. Chobanyan and H. Salehi ). Math Notes (Zamekti). Submitted 10/9/04.
20. On the constant in Menshov-Rademacher inequality (Joint with S.Chobanyan and H. Salehi). Archives of Inequalities and Applications. Submitted 3/8/05.
21. A note on absorbing probabilities in one-dimensional random walk via complex-valued martingales (joint with D. Gilliland and Y. Xaio) Statistics and Probability letter. Submitted 5/6/05.
22. Strong Law of Large numbers under general moment conditions (Joint with S. Chobanyan and H. Salehi ) Electronic Communications in Probability. Submitted 5/31/05.
23. Optimal Sourcing under price uncertainty: A risk averse buyer's perspective (Joint with Santosh Mahapatra and Ram Narasimahan). Accepted at DSI Conference Proceedings, 2005.
24. The behavior of available end to end bandwidth: A non-parametric approach ( Joint with A. Chobanyan, M. Mutka and N. Xi). To be submitted soon.
25. A new probabilistic proof for Von Neumann's mean ergodic theorem via an exact formula for the second moment of the sample mean. To be submitted soon.
07/21/05