随笔分类 -  Math

摘要：一些比较重要的定理公式1) If P and Q are equivalent measures, and Xt is an Ft-adapted process then the followingresults hold: EQ (Xt) = EP (Xt dQ/dP)2) Define dQ/dP = exp( - ∫Θdw-1/2∫Θ2du), denote WP is a BM under measure P, then WtQ = WtP +∫0tΘ du is a BM under measure Q 阅读全文

摘要：找到贴吧一个证明 用夹逼定理http://tieba.baidu.com/p/1300488932# 阅读全文

摘要：Assume X ~ N(µx,σx), Y~ N(µy,σy), corre(X,Y) =ρthen1) E(eXeY) = exp{µx +1/2σ2x +µY+1/2σY2+ρσxσy}2)cov(eX,eY) =exp{µx+1/2σ2x +µY+1/2σY2}(exp{ρσxσy}-1) 阅读全文

摘要：Assume t<u, conditional expectaion follows normal distribution E(Wt|Wu) ~ N[t/uWu, t(u-t)/u]证明与布朗桥有关， 具体可见http://disi.unal.edu.co/~gjhernandezp/mathcomm/slides/bm.pdf 阅读全文