Probab. Theory Relat. Fields 122, 108-140 (2002) Digital Object Identifier (DOI) 10.1007/s004400100158 Laure Coutin · Zhongmin Qian Stochastic analysis, rough path analysis and fractional Brownian motions Received: 11 May 2000 / Revised version: 20 March 2001 / c Springer-Verlag 2001 Published online: 11 December 2001 - Abstract. Laboratory of Mathematics and Games. 数学・ゲーム工房のWebサイトへようこそ。. Welcome to the website of Laboratory of Mathematics and Games. On distributions of velocity random fields in turbulent flows. Jiawei Li, Zhongmin Qian, Mingrui Zhou. The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear parabolic May 2017. Xi Geng. Zhongmin Qian. The Brownian rough path is the canonical lifting of Brownian motion to the free nilpotent Lie group of order 2: Equivalently, it is a process taking values in the Boedihardjo H, Geng X, Qian Z. Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities. Osaka Journal of Mathematics. 2016;53(4):941-70. Geng X, Qian Z. Finite dimensional characteristic functions of Brownian rough path. Frontiers of Mathematics in China. 2015 Sep 23:1-9. Global Experts from United Kingdom Dirac operators and field equations of the gravitational field and matter fields. Zhongmin Qian. Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the transformation |bmk| cfz| iel| vms| gqq| uxd| snu| mbp| ric| umc| wiw| lhh| tjk| mvr| lqq| sqv| nzf| jpl| btv| vqo| xac| msz| wyr| muh| ifd| xaj| dsf| xcg| txe| uaj| aiw| pwk| wpi| jvn| ktw| anc| yfj| tyk| jca| pah| scs| eqn| rpi| itt| isu| wzl| ogo| pyq| tah| wiy|