“随机分析”课第一次自学作业,对应Ioannis Karatzas的书"Brownian Motion and Stochastic Calculus"2.1-2.4节。主要讲Brown运动的三种构造。
Def. (Brownian Motion) A stochastic process{Bt,t≥0}:(1)B0=0;(2)∀0≤t1≤⋯≤tn,Bt1−Bt1,…,Btn−Btn−1are independently distributed;(3)If0≤s≤t,the incrementBt−Bs∼N(0,t−s);(4)With probability 1,t→Bt(ω)is continuous. 其中,前三条可以等价于证明这是一个均值...
[2] IOANNISK,STEVEN E.Shreve,brownian motion and stochastic calculus[M].New York:Spring- Verlag World Publishing corp,1990. [3] BLUMENTHAL R M.Excursions of Markov Processes[M].Birkhauser Boston Inc,1991. [4] 张波.应用随机过程[M].北京:中国人民大学出版社,2001. [5] 徐侃.关于Brow运动的定义...
Journal of Differential Equations, 267(2), 1355-1383. [2] Mao, X. (2008). Stochastic differential equations and applications. Elsevier. [3] Mishura, Y. S. (2008). Stochastic calculus for fractional Brownian motion and related processes. Springer Science & Business Media....
proachingtheprocessinthepropertyofMartingale.Wederiveandanalyzethestageinhavingdividend-payingof theoptionfixedpriceequation. Keywords:martingale;optionpricing;fractionalbrownianmotion;dividends 收稿日期:2009-05-15 基金项目:国家自然科学基金(10771046) 作者简介:于艳娜(1982—),女,硕士研究生,E-mail:yyna5815@...
Fractional Brownian motionNoninstantaneous impulsiveSadovskii fixed point theoremWe introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate ...
Fractional Brownian motionLarge deviations principleWeak convergence approachIn this paper, we are concerned with multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motion (with Hurst indexH>12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{...
ElsevierStochastic Processes and their ApplicationsJ. Hong, C. Huang, M. Kamrani and X. Wang, Optimal Strong Convergence Rate of a Backward Euler Type Scheme for the Cox-Ingersoll-Ross Model Driven by Fractional Brownian Motion, arXiv:1809.04398...