# Personal Information

More >>**
Professor
Supervisor of Doctorate Candidates
Supervisor of Master's Candidates
**

**Other Post:**统计与金融研究所所长

# Profile

Experience Academic Qualifications

1.Post Doctor. in School of Computing Sciences Dalian University of Technology, China, 2010.02—2011.11

2.Jointed PhD. in Department of Mathematics University of Delaware, USA,2007.11—2008.11.

3.Ph.D. in School of Mathematical Sciences Dalian University of Technology, China, 2006.0—2009.11

4.M.S. in School of Mathematical Science, Dalian University of Technology, China, 2004.09—2006.06

5.B.S. in School of Mathematical Scienc Dalian University of Technology, China, 2000.09—2004.06.

Employment

1.Professor, School of Mathematical Sciences, Dalian University of Technology, Dalian, China 2018/12-Present.

2.Associate Professor, School of Mathematical Sciences, Dalian University of Technology, Dalian, China 2013/12-2018/12.

3.Assistant Professor, School of Mathematical Sciences, Dalian University of Technology, Dalian, China 2010/02-2013/12.

4.Scholar visitor in Nanyang Technological University. 2012.05-2012.07 (Invited by Professor Guangming Pan)

5.Research Associate in The Chinese University of Hong Kong. 2016.06-2016.12 (Invited by Professor Qiman Shao)

Research Field

1.The first exit time of Brownian motion;

2.Precise large deviation for sums of random variables;

3.Gamma function; Euler constant.

4.Mills’ Ratio; Gamma Ratio; Beta Ratio.

Social service

2009—Present, Member, Institute of Mathematical Statistics (IMS)

2015—Present, Mathematical Reviews, American Mathematical Society

2015—Present, Reviewer National Natural Sciences Foundation of China

Reviewer for the following journals:

1, Journal of Computational and Applied Mathematics；

2, Applied Mathematics and Computation；

3, Journal of Inequalities and Applications；

4, Journal of Number Theory；

5, Stochastics: An International Journal Of Probability And Stochastic Processes；

6，Integral Transforms And Special Functions；

Research Grants

National Natural Sciences Foundation of China(11101061), PI, 01/01/2012-12/31/2014.

National Natural Sciences Foundation of China(11571058), PI, 01/01/2016-12/31/2019.

National Natural Sciences Foundation of China(11371077), Co-I, 01/01/2014 12/31/2017.

National Natural Sciences Foundation of China(12371154), PI, 01/01/2024-12/31/2027.

Publication （SCI ） *Corresponding Author

**[99], D.Lu* and X.Cai. Precise large deviations for sums of dependent random variables with subexponential distribution.Communications in Statistics – Theory and Methods. Accepted (2024) (SCI)**

**[98], D.Lu* and X.Liu and Y. Wang. Tail bounds for weighted sums of independent Poisson random variables.Communications in Statistics – Theory and Methods. Accepted (2024) (SCI)**

**[97], L. Zhang and D. Lu and H. Cui*. Tail Dependence Matrices and Tests based on Spearman's \rho and Kendall's \tau. Acta Mathematica Sinica, English Series Accpted (2023) (SCI)**

**[96], Y. Zhou and D. Lu*. The first exit time of fractional Brownian motion with a drift from a parabolic domain. Methodology and Computing in Applied Probability. Article: Article:3 26(1)1-19 (2024) (SCI) **

**[95],B.Duan and Yutian Li and Dawei Lu and Yang Lu and Ran Zhang*. Pricing Stocks with Trading Volumes. CSIAM Transactions on Applied Mathematics. 5(1) 1-17(2024) (SCI)**

**[94], D. Lu* and R. Wang. Optimizing the coefficients of the Ramanujan expansion. Journal of Number Theory. 257 146-162 (2024) (SCI)**

[93],B.Duan and Yutian Li and Dawei Lu and Yang Lu and Ran Zhang*. Pricing Stocks with Trading Volumes. CSIAM Transactions on Applied Mathematics. Accept (2023) (SCI)

[92], X.Shen and M.Yuan* and D.Lu. Uniform asymptotics for ruin probabilities of multidimensional risk models with stochastic returns and regular variation claims. Communications in Statistics – Theory and Methods. 52(19) 6878-6895 (2023) (SCI)

[91],Y. Meng and D.Lu*. Asymptotics for atime-dependent by-claim model with dependent subexponential claims. Insurance Mathematics and Economics. 112C. 120-141 (2023) (SCI)

[90], L. Wang and D. Lu*. Application of Bernstein polynomials on estimating a distribution and density function in a triangular array. Methodology and Computing in Applied Probability. 25(2) Article:56 (2023)(SCI)

[89], D. Lu* and H. Lv, A Galton-Watson process with a threshold at 1 and an immigration at 0. Statistics & Probability Letter. 201 109881 (2023) (SCI)

[88], D. Lu* and Q. Liu. Some new Hardy inequalities in probability. FILOMAT.37(21) 7311-7318 (2023) (SCI)

[87], D.Lu*and J.Yang. Identifying the distribution of linear combinations of gamma random variables via Stein's method. Communications in Statistics –Theory and Methods. 52(07) 2116-2123 (2023) (SCI)

[86], D. Lu* and Y. Meng. Complete and complete integral convergence for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations.

Communications in Statistics –Theory and Methods. 52(04) 1273-1286 (2023) (SCI)

[85], D. Lu* and M. Yuan. Asymptotic finite-time ruin probabilities for a bidimensional delay-claim risk model with subexponential claims. Methodology and Computing in Applied Probability. 24(4) 2265-2286 (2022) (SCI)

[84], D. Lu* and Y.Wang and J. Li. On sequential maxima of geometric sample means, with extension to the ruin probability. FILOMAT. 36(17) 5857-5874 (2022) (SCI)

[83], D. Lu* and L.Wang and J. Yang.The stochastic convergence of Bernstein polynomial estimators in a triangular array. Journal of Nonparametric Statistics. 34(04)987-1014 (2022) (SCI)

[82], D. Lu* and Y. Meng. Complete and complete integral convergence for arrays of rowwise widely negative dependent random variables under the sub-linear expectations. Communications in Statistics –Theory and Methods. 51(09) 2994-3007 (2022) (SCI)

[81], D. Lu* and Y. Zhou, The first exit time of fractional Brownian motion from the minimum and maximum parabolic domains. Statistics & Probability Letter. 186 109467 (2022) (SCI)

[80], M. Yuan and D. Lu*. Precise large deviation for sums of sub-exponential claims with the m-dependent semi-Markov type structure. Statistics & Probability Letters. 185 109440 (2022) (SCI)

[79], L. Wang and D. Lu*. On the rates of asymptotic normality for Bernstein density estimators in a triangular array. Journal of Mathematical Analysis and Applications. 511(01) 126063 (2022) (SCI)

[78], D. Lu* and L. Wang. Complete Moment Convergence for the Widely Orthant Dependent Linear Processes with Random Coefficients. Communications in Statistics –Theory and Methods. 51(03) 811-825 (2022) (SCI)

[77], L. Zhang and D. Lu* and X. Wang. The essential dependence for a group of random vectors. Communications in Statistics –Theory and Methods. 50(24) 5810-5846 (2021) (SCI)

[76], D. Lu* and L. Wang. On the rates of asymptotic normality for Bernstein polynomial estimators in a triangular array. Methodology and Computing in Applied Probability. 23(04) 1519-1536 (2021) (SCI)

[75], D. Lu* and J. Cong and Y. Yang. Complete and complete moment convergence for arrays of rowwise asymptotically almost negatively associated random variables under the sub-linear expectations. FILOMAT. 35(2) 633-644 (2021) (SCI)

[74], D. Lu* and J. Wang. Complete convergence and complete moment convergence for maximal randomly weighted sums of widely orthantdependent random variables with applications. Communications in Statistics –Theory and Methods. 50(04) 763-791 (2021) (SCI)

[73], L. Zhang and D. Lu* and X. Wang. Measuring and testing interdependence among random vectors based on Spearman's $\rho$ and Kendall's $\tau$. Computational Statistics. 35(4) 1685-1713 (2020) (SCI)

[72], D. Lu* and Q. Liu and X. Shen. Some improved tail bounds for the sum of variables with geometric distribution. Communications in Statistics – Theory and Methods. 49(22) 5427-5435 (2020) (SCI)

[71], X. Shen* and Q. Liu and D. Lu. Ruin Problems of multidimensional risk models under constant interest rates and dependent risks with heavy tails. Mathematical Problems in Engineering, ID 9489612 (2020)

[70], D. Lu* and X. Chen and J. Feng. Moderate deviations for the random weighted sums of WUOD random variables with consistently varying tails. Communications in Statistics – Theory and Methods. 49(03) 531-551 (2020) (SCI)

[69],D. Lu* and J. Du and H. Song. Some asymptotic results of the ruin probabilities in a bidimensional renewal risk model with Brownian perturbation. FILOMAT. 33(10) (2019) (SCI)

[68],D. Lu* and H. Xu and Y. Niu. A new general asymptotic formula for the Mills' ratio of the skew-generalized normal distribution. Journal of Mathematical Analysis and Applications. 48(01) 123378 (2019) (SCI)

[67], D. Lu and L. Song* and F. Li. Uniform asymptotics for discounted aggregate claims in dependent multi-risk models. Communications in Statistics - Theory and Methods. 48(04) 781-793 (2019)

[66], H. Wang* and Q. Zhang and D. Lu. A quicker approximation of the gamma function towards the Windschitl’s formula by continued fraction. The Ramanujan Journal. 48(1) 75-90 (2019)

[65], D. Lu and X. Wang* and R. Xu. Some new exponential-function estimates of the Somos' quadratic recurrence constant. Results in Mathematics. 74(1), UNSP 6 (2019)

[64], J. Feng and D. Lu* and Z. Wen. Some new sequences and inequalities related to Euler's constant. Results in Mathematics. 73(4), UNSP 158 (2018)

[63], D. Lu* and L. Zhang and X. Wang and L. Song. Some new measures of dependence for random variables based on Spearman’s ρ and Kendall’s τ.Journal of Nonparametric Statistics. 30(04) 860-883 (2018)

[62], D. Lu* and L. Song and H. Li. Precise large deviations for sums of WUOD and

Φ-mixing random variables with dominated variation. Communications in Statistics – Theory and Methods. 47(19), 4791-4807 (2018)

[61], X. Wang* and D. Lu and L. Song. Robust image segmentation via Bayesian type criterion. Communications in Statistics - Theory and Methods. 47(17), 4215-4228 (2018)

[60], S. Fang and L. Lai and D. Lu* and X. Wang. On some convergence to the constant $e$ and proof of Keller's limit. Results in Mathematics. 73(2), UNSP 69 (2018)

[59]，D. Lu and X. Wang and L. Song* and H. Xu. A new continued fraction approximation and inequalities for the Gamma function via the Tri-gamma function. The Ramanujan Journal. 46(1),119-125 (2018)

[58], X. Hu and D. Lu and X. Wang*. New quicker sequences and inequalities with continued fraction towards Euler's constant. Results in Mathematics. 73(1), UNSP 28 (2018)

[57], D. Lu and L. Song* and G. Tang. Some new approximations and proofs for Mills’ ratio. Results in Mathematics. 73(1), UNSP 27 (2018)

[56], D. Lu and L. Song* and X. Wang and J. Wang. New asymptotic formulas and inequalities for the gamma function based on continued fractions. Results in Mathematics. 73(1), UNSP 37 (2018)

[55], D. Lu* and X. Wang and J. Wei. Continued fractions and inequalities about $\left(1+\frac{1}{x}\right)^x$. Results in Mathematics. 72(4),2241-2252(2017)

[54], D. Lu* and T. Qu and X. Wang. A kind of new continued fraction approximation of Gamma function based on Mortici’s formula. Results in Mathematics. 72(3) , 1417-1436 (2017)

[53], D. Lu and L. Song* and Q. Xu. New continued fraction expansions and inequalities for $n!$ into negative powers of a triangular number. Results in Mathematics. 72(1-2),765-786(2017) (SCI)

[52], D. Lu and L. Song* and J. Wang. Some asymptotic formulas and inequalities about gamma and psi functions based on continued fractions. Results in Mathematics.72(1-2),225-238 (2017) (SCI)

[51], D. Lu* and S. Liu. Improved convergence towards Glaisher-Kinkelin's and Bendersky-Adamchik's constants. Results in Mathematics. 71(3), 731-747 (2017) (SCI)

[50], D. Lu and L. Song* and Z. Liu. Some new approximations and inequalities of the sequence (1 + 1/n)^n and improvements of the Carlemans’ inequality. The Ramanujan Journal. 43(1), 69-82 (2017) (SCI)

[49], D. Lu* and X. Qi. Precise large deviations for $\phi$-mixing and UND random variables with long-tailed distributions. Communications in Statistics - Theory and Methods. 46(11), 5443-5452 (2017) (SCI)

[48], D. Lu* and S. Liu. Some new convergent sequences of Glaisher-Kinkelin's and Bendersky-Adamchik's constants. Results in Mathematics. 71(1), 225-240 (2017) (SCI)

[47], D. Lu* and X. Liu and T. Qu. Continued fraction approximations and inequalities for the gamma function by Burnside. The Ramanujan Journal. 42, 491-500 (2017) (SCI)

[46], D. Lu and L. Song* and Y. Yu. Some quicker continued fraction approximations and inequalities towards Euler's constant. Journal of Number Theory. 175, 100-116 (2017) (SCI)

[45], L. Song and Z. Huang and D. Lu* and X. Qi. Precise large deviations for the difference of two sums of WUOD and non-identically distributed random variables with dominatedly varying tails. Communications in Statistics - Theory and Methods. 46(4), 2013-2028 (2017) (SCI)

[44], Z. Hua and L. Song and D. Lu* and X. Qi. Precise large deviations for the difference of two sums of END random variables with heavy tails.Communications in Statistics - Theory and Methods. 46(2), 736-746 (2017) (SCI)

[43], D. Lu* and P. Zhang. A new general asymptotic formula and inequalities involving the volume of the unit ball. Journal of Number Theory. 170，302-314.(2017) (SCI)

[42], X. Liu and D. Lu and L. Song*. Some quicker approximations and inequalities of the Wallis ratio by continued fraction. Results in Mathematics. 70(3), 325-335 (2016) (SCI)

[41], D. Lu*. Some asymptotic formulas of a Brownian motion with regular variation from the maximum and minimum complicated domains. Communications in Statistics - Theory and Methods. 45(22), 6569-6595 (2016) (SCI)

[40], D. Lu*. Certain approximations to achieve sharp lower and upper bounds for the Mills' ratio of the inverse Gaussian distribution. Journal of Mathematical Analysis and Applications. 444, 737-744 (2016) (SCI)

[39], D. Lu and L. Song* and C. Ma. A quicker continued fraction approximation of the gamma function related to the Windschitl's formula. Numerical Algorithms. 72:865–874 (2016) (SCI)

[38], D. Lu* and B. Zhang. Some asymptotic results of the ruin probabilities in a two dimensional renewal risk model with some strongly subexponential claims. Statistics & Probability Letters. 114, 20-29 (2016) (SCI)

[37], D. Lu* and L. Song and T .Zhang. Large deviations for sum of UEND and $\phi$-mixing random variables with heavy tails. Communications in Statistics - Theory and Methods. 45(7), 2118-2129 (2016) (SCI)

[36], D. Lu*. A note on the estimates of multivariate Gaussian probability. Communications in Statistics - Theory and Methods. 45(5), 1459-1465 (2016) (SCI)

[35], D. Lu and C. Mortici and L. Song*. Some new approximations of Glaisher-Kinkelin’s and Bendersky-Adamchik’s constants by continued fraction. Journal of Number Theory. 163, 434-448. (2016) (SCI)

[34], D. Lu* and L. Song and X. Wang. Precise large deviation for the difference of two sums of random variables. Communications in Statistics - Theory and Methods. 45(2), 291-306. (2016) (SCI)

[33], D. Lu* and C. Ma. Some new quicker continued fraction approximations for the gamma function related to the Nemes’ formula. Numerical Algorithms. 70(4), 825-833. (2015) (SCI)

[32], D. Lu*. Some asymptotic formulas for a Brownian motion from the maximum and minimum complicated domains. Communications in Statistics - Theory and Methods. 44(15)，3192-3217. (2015)（SCI）

[31], D. Lu and L. Song*. Some asymptotic formulas for a Brownian motion with a regular variation from a parabolic domain. Communications in Statistics - Theory and Methods. 44(9)，1763-1778. (2015) (SCI)

[30], D. Lu* and Z. Song. Some new continued fraction estimates of the Somos' quadratic recurrence constant. Journal of Number Theory. 155，36-45. (2015) (SCI)

[29], D. Lu* and L. Song and Y. Yu. New sequences with continued fraction towards Euler's constant. Applied Mathematics and Computation. 259，12-20. (2015) (SCI)

[28], D. Lu and L. Song* and C. Ma. Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula. Applied Mathematics and Computation. 253，1-7. (2015) (SCI)

[27], D. Lu* and L. Song and Y. Yu. Some new continued fraction approximation of Euler's constant. Journal of Number Theory. 147，69-80. (2015) (SCI)

[26], D. Lu*. A new sharp approximation for the Gamma function related to the Burnside's formula. The Ramanujan Journal. 35 (1)，121-129. (2014) (SCI)

[25], D. Lu*. Some Asymptotic Formulas for a Brownian Motion from The Maximum and Minimum Domains with Regular Varying Boundary. Communications in Statistics - Theory and Methods. 43(18), 3848-3865. (2014) (SCI)

[24], D. Lu* and J. Feng and C. Ma. A general asymptotic formula of the gamma function based on the Burnside's formula. Journal of Number Theory. 145，317-328. (2014) (SCI)

[23], D. Lu* and C. Mortici.Some new quicker approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants. Journal of Number Theory. 144, 340-352. (2014) (SCI)

[22], D. Lu*. Some new improved classes of convergence towards Euler's constant. Applied Mathematics and Computation. 243, 24-32. (2014) (SCI)

[21], D. Lu*. Some new convergent sequences and inequalities of Euler's constant. Journal of Mathematical Analysis and Applications. 419 (1), 541-552. (2014) (SCI)

[20], C. Mortici*. V. G. Cristea. D. Lu. Completely monotonic functions and inequalities associated to some ratio of gamma function. Applied Mathematics and Computation. 240, 168-174. (2014) (SCI)

[19], D. Lu* and X. Wang. A new asymptotic expansion and some inequalities for the Gamma function. Journal of Number Theory. 140, 314-323. (2014) (SCI)

[18], D. Lu* and L. Song and C. Ma. A generated approximation of the gamma function related to Windschitl's formula. Journal of Number Theory. 140, 215-225.(2014) (SCI)

[17], L. Song and D. Lu* and F. Liu. Using convex combination of copulas and EM algorithm for credibility. Communications in Statistics - Theory and Methods. 43(6), 1222-1233. (2014) (SCI)

[16], D. Lu* and X. Wang, Some new normal comparison inequalities related to Gordon's inequality. Statistics & Probability Letter. 88, 133-140. (2014). (SCI)

[15], D. Lu*. Some quicker classes of sequences convergent to Euler's constant. Applied Mathematics and Computation. 232, 172-177. (2014) (SCI)

[14], D. Lu*. A generated approximation related to the Burnside's formula. Journal of Number Theory. 136, 414-422. (2014) (SCI)

[13], D. Lu*. A new quicker sequence convergent to Euler's constant. Journal of Number Theory. 136, 320-329. (2014) （SCI）

[12], D. Lu* and L. Song and Y. Xu. Precise large deviations for sums of independent random variables with consistently varying tails. Communications in Statistics - Theory and Methods. 43(1), 28-43. (2014) (SCI)

[11], L. Song and W. Che and D. Lu*. The exit probabilities of Brownian motion with variable dimension applying to the control of population growth. International Journal of Biomathematics. 6(5) 1–12. (2013) (SCI)

[10], D. Lu* and X. Wang. A Generated approximation related to the Gosper's formula and the Ramanujan's formula. Journal of Mathematical Analysis and Applications . 406 287-292. (2013) (SCI)

[09], X. Wang* and D. Lu and L. Song. Statistical Inference for Partially Linear Stochastic Models with Heteroscedastic Errors. Computational Statistics and Data Analysis. 66 150-160. (2013). (SCI)

[08], D. Lu*. Lower bounds of large deviation for sums of long-tailed claims in a multi-risk model. Statistics & Probability Letter，82 (7) 1242-1250. (2012) (SCI)

[07], D. Lu* and J. Feng and X. Liang. A note on the estimate of the beta distribution. Mathematical Inequalities & Applications. 15 (4) 859–870. (2012) (SCI)

[06], D. Lu* and L.Song and Y. Wang. A note on the estimate of Gamma distribution. Mathematical Inequalities & Applications. 15 (1) 217–227. (2012) (SCI)

[05], D. Lu* and L. Song, The asymptotic behavior of a Brownian motion with a drift from a random domain. Communications in Statistics - Theory and Methods. 41(1), 62-75. (2012) (SCI)

[04], D. Lu*, Lower and upper bounds of large deviation for sums of subexponential claims in multi-risk model. Statistics & Probability Letter. 81 (12) 1911-1919. (2011). (SCI)

[03], D. Lu* and L. Song, The First Exit Time of a Brownian Motion from The Minimum and Maximum Parabolic Domains. Journal of Theoretical Probability. 24 (4) 1028-1043. (2011) (SCI)

[02], D. Lu* and W.V. Li, A Note on Multivariate Gaussian Estimates. Journal of Mathematical Analysis and Application. 354 704-707. (2009) (SCI)

[01], L. Song, D. Lu* and J. Feng, The first exit time for a Bessel process from the minimum and maximum random domains. Statistics & Probability Letter. 79 (20) 2115-2123. (2009) (SCI)

# Educational Experience

# Work Experience

# Research FocusMore>>

- Mills’ Ratio; Gamma Ratio; Beta Ratio

- Gamma function; Euler constant

- Precise large deviation for sums of random variables