个人简介
Education
Ph.D., Fudan University, Department of Mathematics, 1997
M.S., Northwest University/Henan Normal University, Department of Mathematics, 1990
B.S., Henan Normal University, Department of Mathematics, 1983
Professional Experience
2004-Now, Professor, East China Normal University, Department of Mathematics
1999-2004, Associate Professor, East China Normal University, Department of Mathematics
2003-2004, Postdoctoral Fellow, BarIlan University, Israel, Department of Physics
1997-1999，Postdoctoral Fellow, Zhejiang University, Department of Mathematics
1990-1994, Lecturer, Henan Normal University, Department of Mathematics
近期论文
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The Hausdorff dimension and measure of the generalized Moran fractals and Fourier series (with F.-Y. Ren), Chin. Ann. of Math. B 16 (2) (1995) 153-162.
The multifractal analysis of probability measure on the generalized Moran sets (with H. Shen), Chin. J. of Contemporary Math. 16 (4) (1995) 403-414.
The Fourier series expansions of functions defined on s-sets (with W.-S. Li, F. Su, F.- Y. Ren), Chin. Ann. of Math. (B) 18 (2) (1997) 201-212.
The study of the Fourier series of functions defined on Moran fractals (with F.-Y. Ren), Acta Mathematicae Appicatae Sinica, 13(2) (1997) 158-166.
Hausdorff dimensions of random net fractals (with F.-Y. Ren), Stochastic Processes and Their Applications, 74 (1998) 235-250.
On three open questions proposed by Falconer (with X.-T. Wang, F.-Y. Ren), Progress in Natural Science, Vol. 9 (3) (1999) 180-188.
Multifractal decompositions of random net fractals (with F.-Y. Ren, X.-J. Xu), Chin. Ann. of Math. A, 20 (1) (1999), 81-90 (in Chinese).
The determination of the diffusion kernel on fractals and fractional diffusion equation for transport phenomena in random media (with F.-Y. Ren, X.-T. Wang), Physics Letters A, 252 (1999) 141-150.
Hausdorff dimension, mean quadratic variation of infinite self-similar measure (with Z.- G. Yu, F.-Y. Ren), Bull. Of the Hongkong Math. S., 2 (1999) 347-355.
Measures and their dimension spectrums for cookie-cutter sets in Rd (with Z.-G. Yu, F.-Y. Ren), Acta Mathematicae Applicatae Sinica, 16 (1) (2000) 9-21.
The non-integer operation associated to random variation sets of the self-similar sets (F.-Y. Ren), Physica A 286 (2000) 45-55.
] Determination of diffusion kernel on fractals (with F.-Y. Ren, X.-T. Wang), J. Phys A: Math. Gen. 34 (2001) 9815-9825.
Determination of memory function and flux on fractals (with F.-Y. Ren, W.-Y. Qiu, X.- T Wang), Physics Letters A 288 (2001) 79-87.
A proof for French’s empirical formula on option pricing (with F.-Y. Ren, X.-T. Wang), Chaos, Solitons and Fractals 12 (2001) 2441-2453.
Random Markov-self-similar measures, Stochastic Processes and Their Applications, 98 (2002) 113-130.
Universality of stretched Gaussian asymptotic behavior for the fractional Fokker– Planck equation in external force fields (with F.-Y. Ren, W.-Y. Qiu, Y. Xu), J. Phys. A: Math. Gen. 36 (2003) 7533-7543.
Integrals and derivatives on net fractals (with F.-Y. Ren, X.-T. Wang, W.-Y. Qiu), Chaos, Solitons & Fractals, 16 (1) (2003) 107-117.
Fractional Fokker–Planck equation on heterogeneous fractal structures in external force fields and its solutions (with F.-Y. Ren, W.-Y. Qiu, Y. Xu), Physica A: Statistical Mechanics and its Applications, 326 (2003) 430-440.
An anomalous diffusion model in an external force fields on fractals (with F.-Y. Ren, W.-Y. Qiu, X.-T. Wang, Y. Xu, R. R. Nigmatullin), Physics Letters A, 312 (2003) 187-197.
Stretched Gaussian asymptotic behavior for fractional Fokker-Planck equation on fractal structure in external force fields (with Y. Xu, F.-Y. Ren, W.-Y. Qiu), Chaos, Soliton and Fractals, 20 (2004) 591-506.
Answer to an open problem proposed by E Barkai (with F.-Y. Ren, W.-Y. Qiu, Y. Xu), J. Phys. A: Math. Gen. 37 (2004) 9919–9922.
Stretched Gaussian Asymptotic Behavior for Fractional Giona–Roman Equation on Biased Heterogeneous Fractal Structure in External Force Fields (with F.-Y. Ren, W.-Y. Qiu, Y. Xu)，Nonlinear Dynamics 38 (2004) 285–294.
Scaling of Horizontal and Vertical Fixational Eye Movements (with S. Moshel, Ari Z. Zivotofsky, Avi Caspi, R. Engbert, R. Kliegl and S. Havlin), Physical Review E, 71 (2005) 031909.
Phase synchronization decay of fixational eye movements (with S. Moshel, Ari Z. Zivotofsky, R. Engbert, R. Kliegl, S. Havlin)，Annals of the New York Academy of Sciences, 1039 (2005) 484-488.
Universality of stretched Gaussian asymptotic diffusion behavior on biased heterogeneous fractal structure in external force fields (with F.-Y. Ren, Y. Xu, W.-Y. Qiu), Chaos, Solitons & Fractals, 24 (2005) 273-278.
Answer to an open problem proposed by R Metzler and J Klafter (with F.-Y. Ren, W.- Y. Qiu, J.-B. Xiao), J. Phys. A: Math. Gen. 39 (2006) 4911–4919.
Asymptotic behavior of a fractional Fokker–Planck-type equation (with F.-Y. Ren, W.- Y. Qiu, J.-B. Xiao), Physica A 373 (2007) 165–173.
Exact solutions for nonlinear fractional anomalous diffusion equations (with F.-Y. Ren, W.-Y. Qiu, J.-B. Xiao), Physica A 385 (2007) 80–94.
Fractional nonlinear diffusion equation and first passage time (with J. Wang, W.-J. Zhang, J.-B. Xiao, F.-Y. Ren), Physica A, 387 (2008) 764-772.
Solutions of fractional nonlinear diffusion equation and first passage time: influence of initial condition and diffusion coefficient (with J. Wang, W.-J. Zhang, P. Zhang, F.-Y. Ren), Physica A, 387 (2008) 4547-4552.
The solutions to a Bi-fractional Black-Scholes-Merton differential equation (with J. Wang, W.-J. Zhang, W.-Y. Qiu, F.-Y. Ren), International Journal of Pure and Applied Mathematics, 58 (1) (2010) 99-112.
Option pricing of a bi-fractional Black–Merton–Scholes model with the Hurst exponent H in (with J. Wang, W.-J. Zhang, W.-Y. Qiu, F.-Y. Ren), Applied Mathematics Letters, 23 (8) (2010) 859-863.
Exact solutions for nonlinear Fokker- Planck equations (with F.-Y. Ren), 2010.
Fractional Fokker-Planck Equation and Black-Scholes Formula in Composite-Diffusive Regime (with J. Wang，L.-J. Lv，H. Gu，W.-Y. Qiu，F.-Y. Ren)，J Stat Phys, 146 (2012) 205–216.
Time-changed geometric fractional Brownian motion and option pricing with transaction costs (with H. Gu, Y.-X. Zhang), Physica A, 391 (2012) 3971–3977.
On a time-changed geometric Brownian motion and its application in financial market (with H. Gu, Y.-X. Zhang), Acta Physica Polonica B, 43 (2012) 1667-1681.
Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime (with J. Wang, L.-J. Lv, W.-Y. Qiu, F.-Y. Ren), Physica A 391 (2012) 750–759.
Fokker-Planck type equations associated with subordinated processes controlled by tempered alpha-stable processes (with Y.-X. Zhang, H. Gu), Journal of Statistical Physics, 152 (2013) 742-752.
Equivalence of subordinated processes with tempered alpha-stable waiting times and fractional Fokker-Planck Equations in space and time dependent fields (with Y.-X. Zhang, H. Gu), J. Stat. Phys., 159 (2015) 1495-1503.
Fokker-Planck-type equations corresponding to a class of compound process, 2016
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