# Wenbo V. Li

• On the Number of Switches in Unbiased Coin-tossing
• Gambler's ruin problems with moving boundaries, (with P. Devlin).
• A generic method for problems of random assignment type. In preparation.
• Karhunen-Loeve expansions for non-tensored Gaussian fields, (with X. Ai and Z. Dong).
• Bounds between small value probability and Laplace transform.
• On a family of symmetrization inequalities, (with Z. Dong and J. Li).
• Gaussian Inequalities and Conjectures
• Independent constants and some Gaussian inequalities
• Recent advances in Chung's LIL (Not the Other LIL)
• No chance for families of random polynomials to have all real roots, (with P. Devlin, M. Xu and Y. Yao)
• A note on small value probability for intersection local times, (with X. Chen).
• Small value probabilities for Galton-Watson processes with immigration, (with W. Chu, and Y. Ren), to appear in Bernoulli
• Minimum volume for intersection of symmetric convex body and its rotations, (with S. Zhang).
• Determinant estimates for positive definite matrices, (with F. Gao).
• On a family of Gaussian processes and the positivity exponent of random polynomials, (with Q. Shao).
• Integral representations for binomial sums of chances of winning, (with Z. Dong and C. Song),
• Nonsymmetric matrices with all real eigenvalues, (with Y. Leung).
• Spectral analysis of a class of non-reversible Markov Chains, (with Y. Leung).
• On solutions of Ax=1/x for a positive semi-definite matrix A, (with Y. Leung and Rakesh)
• Fastest rate of convergence for Brownian motion with jump boundary, (with Y. Leung),
• Diffusions with holding and jumping boundary, (with J. Peng), to appear in Science in China Ser, A.
• Pricing and hedging of cliquet options and locally-capped contracts (with C. Bernard), to appear in SIAM Journal on Financial Mathematics.
• Probabilities of all real zeros for random polynomials,
• Small ball probability for a family of smooth Gaussian processes, (with F. Aurzada, F. Gao, T. Kuhn, and Q. Shao), to appear in Journal of Theoretical Probability.
• Karhunen-Loeve expansions for the detrended Brownian motion, (with X. Ai and G. Liu), Statistics and Probability Letter, Vol 82, 1235–1241, (2012).
• Small value probabilities for supercritical continuous state branching processes with immigration, (with W. Chu and Y-X. Ren), Science in China Ser, A. Vol. 55, 2259–2271, (2012).
• Probabilities of competing binomial random variables, (with V. Vysotsky), Journal of Applied Probability, Vol 49, 731-744 (2012).
• A Gaussian inequality for expected absolute products, (with A. Wei), Journal of Theoretical Probability, Vol. 25, 92-99 (2012).
• Wick formulas for quaternion Gaussian and $\beta$-permanental variables, (with A. Wei), Stochastic analysis and its applications, Series of Interdisciplinary Mathematical Sciences, ed. by T. Zhang and X. Zhou, p291-300, (2012).
• Stationary weak solutions for stochastic 3D Navier-Stokes equations with Levy noise, (with Z. Dong and J. Zhai), Stochastics and Dynamics} Vol. 12, No. 1 (2012) 1150006 (22 pages), DOI: 10.1142/S0219493712003559.
• Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes, (with X. Chen, J. Rosinski, Q.M. Shao), Ann. Prob. Vol 39, 729-778, (2011)
• How many Laplace transforms of probability measures are there? (with F. Gao and J. Wellner), Proceedings of the American Mathematical Society, Vol 138, 4331-4344, (2010).
• On the supremum of certain family of stochastic processes, (with N. Pillai and R. Wolpert), Statistics and Probability Letters, Vol 80, 916-921, (2010).
• Expected lengths of minimum spanning trees for non-identical edge distributions, (with X. Zhang), Electronic Journal of Probability, Vol 15, 110-141, (2010).
• A CLT for the $L^{2}$ modulus of continuity of Brownian local time, (with X. Chen, M. Marcus and J. Rosen), Annals of Probability, Vol 38, 396-438, (2010).
• Semiparametric bounds of mean and variance for exotic options, (with Q. Liu), Science in China Ser, A. Vol 52, 1446-1458, (2009).
• Moment bounds for truncated random variables. (with Q. Liu), Statistics and Probability Letters, Vol 79, 1951-1956, (2009).
• Gaussian integrals involving absolute value functions, (with Ang Wei), IMS Collections, High Dimensional Probability V: The Luminy Volume, Vol. 5, 43–59, (2009).
• On the difference of expected lengths of minimum spanning tree, (with X. Zhang), Combinatorics, Probability and Computing, Vol 18, 423-434, (2009).
• A note on Multivariate Gaussian estimates, (with D. Lu), Journal of Mathematical Analysis and Applications, Vol 354, 704-707, (2009).
• On the expected number of zeros of random harmonic polynomials, (with Ang Wei), Proceedings of the American Mathematical Society, Vol 137, 195-204, (2009).
• The d-th linear polarization constant of R^d, (with Y. Leung and Rakesh), Journal of Functional Analysis, Vol 255, 2861-2871, (2008).
• Spectral analysis of Brownian motion with jump boundary, (with Y. Leung and Rakesh), Proceedings of the American Mathematical Society. Vol 136, 4427-4436, (2008).
• Metric entropy of high dimensional distributions and small deviation probability of Brownian sheets, (with R. Blei and F. Gao), Proceedings of the American Mathematical Society, Vol 135, 4009-4018, (2007).
• Optimal ellipsoids and decomposition of positive definite matrices, (with Y. Leung and Rakesh), Journal of Mathematical Analysis and Applications, Vol 331, 1452-1466, (2007).
• Small deviation probabilities for Slepian Gaussian random fields, (with F. Gao), Transactions of the American Mathematical Society, Vol 359, 1339-1350, (2007).
• Logarithmic Level Comparison for small deviation probabilities, (with F. Gao), Journal of Theoretical Probability, Vol 19, 535-556, (2006).
• An analysis of the last round matching problem, (with F. Liu and X. Shi), Journal of Mathematical Analysis and Applications, Vol 323, no. 2, 1373--1382, (2006).
• Large deviations for local times of stable processes and stable random walks in $1$ dimension, (with X. Chen and J. Rosen), {\it Electronic Journal of Probability} Vol. 10, Paper no. 16, 577-608, (2005).
• A functional LIL for stochastic integrals and the Levy area process, (with J. Kuelbs), Journal of Theoretical Probability, Vol 18, 261-290, (2005).
• Recent developments on lower tail probabilities for Gaussian processes, (with Q. Shao), COSMOS, the Journal of the Singapore National Academy of Science, Vol. 1, 95-106, (2005).
• Lower tail probabilities of Gaussian processes, (with Q. Shao), Annals of Probability, Vol 32, 216-242, (2004).
• Small deviations of stable processes via metric entropy, (with W. Linde), Journal of Theoretical Probability, Vol 17, 261-284, (2004).
• Large and moderate deviations for intersection local times, (with X. Chen), Probability Theory and Related Fields, Vol 128, 213-254, (2004).
• Small deviation estimates for some additive processes, (with X. Chen), Progress in Probability}, Vol 55, 225-238, (2003).
• The first exit time of Brownian motion from unbounded convex domain, Annals of Probability, Vol. 31, 1078-1096, (2003).
• Quadratic functionals and small ball probabilities for the m-fold integrated Brownian motion, (with X. Chen), Annals of Probability, Vol. 31, 1052-1077, (2003).
• Limiting behaviors for Brownian motion reflected on Brownian motion, (with X. Chen), Methods and Applications of Analysis, Vol 9, 377-392, (2002).
• A normal comparison inequality and its applications, (with Q. Shao), Probability Theory and Related Fields. Vol. 122, 494-508, (2002).
• A functional LIL and some weighted occupation measure results for fractional Brownian motion, (with J. Kuelbs), Journal of Theoretical Probability, Vol 15, 1007-1030, (2002).
• Capture time of Brownian persuits, (with Q. Shao), Probability Theory and Related Fields, Vol. 121, 30-48, (2001).
• Small ball probabilities for Gaussian Markov processes under the Lp-norm, Stochastic Processes and Their Applications. Vol 92, 87-102, (2001).
• Gaussian processes: Inequalities, small ball probabilities and applications (with Qi-Man Shao), Stochastic processes: Theory and methods, Handbook of Statistics, Vol. 19, Edited by C.R. Rao and D. Shanbhag, 533-598, Elsevier, New York (2001).
• Localization of Majorizing Measures, (with B. B\"uhler and W. Linde), Asymptotic Methods in Probability and Statistics with Applications, 81-100, Birkhauser (2001).
• A functional LIL for symmetric stable processes, (with X. Chen and J. Kuelbs), Ann. Probab. Vol 28, 258-276, (2000).
• A note on the Gaussian correlation conjecture, (with Q. Shao), Progress in Probability, Vol. 47, 163-171, Birkh\"auser (2000).
• Metric Entropy of Convex Hulls in Hilbert spaces, (with W. Linde). Studia Mathematica. Vol. 139, 29-45, (2000).
• Small Ball Probabilities of Integrals of Weighted Brownian Motion, (with T. Dunker and W. Linde), Stat. and Prob. Letters. Vol. 46, 211-216, (2000).
• Approximation, Metric Entropy and Small Ball Estimates for Gaussian Measures, (with W. Linde), Ann. Probab. Vol. 27, 1556-1578, (1999).
• A Gaussian correlation inequality and its applications to small ball probabilities. Electronic Commun. in Probab. Vol. 4, 111-118, (1999).
• Small Deviations for Gaussian Markov Processes under the sup-norm. Journal of Theoretical Probability, Vol. 12, 971-984, (1999).
• Small ball estimates for Gaussian processes under Sobolov type norm, (with Q. Shao). Journal of Theoretical Probability, Vol 12, 699-720, (1999).
• A lim inf result for the Brownian motion, Asymptotic Methods in Probability and Statistics, edited by B. Szyszkowicz. page 281-292, North-Holland, Amsterdam. (1998)
• Random walks on rooted trees, (with F. Lazebnik and R. Martin), The Bulletin of the Institute of Combinatorics and its Applications, Vol. 22 59-66, (1998).
• A central limit theorem for the sock--sorting problem, (with G. Pritchard), Progress in Probability, Vol. 43, 245-248, Birkh\"auser (1998).
• Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables, (with P. Hitczenko, S. Kwapien, G. Schechtman, T. Schlumprecht and J. Zinn), Electronic Journal of Probability Vol. 3, Paper no. 2, 1-26, (1998).
• Some shift inequalities for Gaussian measures, (with J. Kuelbs), Progress in Probability, Vol. 43, 233-243, Birkh\"auser (1998).
• Existence of Small Ball Constants for Fractional Brownian Motions, (with W. Linde), C.R. Acad. Sci. Paris, Vol. 326, 1329-1334, (1998).
• Some remarks on the variation of curve length and surface area. (with J. Kuelbs), Proceedings of American Mathematical Society, Vol. 124, 859-867, (1996).
• An extension of Ehrhard's Theorem. (with J. Kuelbs), Interaction Between Functional Analysis, Harmonic Analysis, and Probability. Lecture notes in pure and applied mathematics. Vol. 175, 291-300, (1996).
• Small ball probabilities for Gaussian processes with stationary increments under Holder norms. (with J. Kuelbs and Q. Shao), Journal of Theoretical Probability, Vol. 8, 361-386, (1995).
• Lim inf results for Gaussian samples and Chung's functional LIL. (with J. Kuelbs and M. Talagrand), Annals of Probability, Vol. 22, 1879-1903, (1994).
• Gaussian samples approach `smooth points' slowest. (with J. Kuelbs), Journal of Functional Analysis, Vol. 124, 333-348. (1994).
• Some large deviation results for Gaussian measures. (with J. Kuelbs), Progress in Probability, Vol. 35, 251-270, Birkhauser (1994).
• On the future infima of some transient processes. (with D. Khoshnevisan and T. Lewis), Probability Theory and Related Fields, Vol. 99, 337-360. (1994).
• The Gaussian measure of shifted balls. (with J. Kuelbs and W. Linde), Probability Theory and Related Fields, Vol. 98, 143-162, (1994).
• Small ball problems for non-centered Gaussian measures. (with W. Linde), Probability and Mathematical Statistics, Vol. 14, Fasc.2, 231-251. (1993).
• Metric entropy and the small ball problem for Gaussian measures. (with J. Kuelbs), Journal of Functional Analysis, Vol. 116, 133-157. (1993).
• Small ball estimates for Brownian motion and the Brownian sheet, (with J. Kuelbs), Journal of Theoretical Probability, Vol. 6, 547-577. (1993).
• How long does it take to see a flat Brownian path on the average? (with T. Lewis), Statistics and Probability Letters, Vol. 16, 347-354, (1993).
• Metric entropy and the small ball problem for Gaussian measures (with J. Kuelbs), C.R. Acad. Sci. Paris, Vol. 315, 845-850, (1992).
• On the lower tail of Gaussian measures on $l_p$. Progress in Probability, Vol. 30, 106-117, (1992).
• Limit theorems for the square integral of Brownian motion and its increments. Stochastic Processes and Their Applications, Vol. 41, 223-239, (1992).
• Lim inf results for the Wiener process and its increments under the $L_2$-norm. Probability Theory and Related Fields, Vol. 92, 69-90, (1992).
• Comparison results for the lower tail of Gaussian seminorms. Journal of Theoretical Probability, Vol. 5, 1-31, (1992).

• Last modified July. 2000 by Wenbo V. Li,
wli@math.udel.edu