本文给出了Bihari不等式成在高维空间的一种推广形式。即证明了定理:设Ω_r表R^n中的球;S^2=sum from i=1 to n (S_i^2≤r^2),Q为R^n中有界可测集,u(s,x),f(s,x)为Ω_R×Q(R>r)下的非责有界连续函数,c≥0为常数,若 u(t,y≤c+∫f(...本文给出了Bihari不等式成在高维空间的一种推广形式。即证明了定理:设Ω_r表R^n中的球;S^2=sum from i=1 to n (S_i^2≤r^2),Q为R^n中有界可测集,u(s,x),f(s,x)为Ω_R×Q(R>r)下的非责有界连续函数,c≥0为常数,若 u(t,y≤c+∫f(s,x)φ[u(s,x)dxds] (1)对(t,y)∈Ω_r×Q(r<R)成立,其中φ(u)当0<u<ü(ü≤∞)为正的连续非减函数,又设ψ(u)=integral from n=0 to u du_1/(φu_1)(c<u<ü)这时如果 ∫Ω_r×Q~[f(s,x)dxds]<ψ(ü-0) (2)则有 supu(t,y)≤ψ^(-1)[f(s,x)dxds] (t,y)∈Ω_r×Q展开更多
本文讨论在金融中有重要应用价值的,由Lévy过程驱动的倒向双重随机微分方程: Y_t=ξ+∫_t^T f(s,Y_(s-),U_s,Z_s)ds+∫_t^T g(s,Y_(s-),U_s,Z_s)dB_s -∫_t^TU_sdW_s-sum for i=1 to ∞ Z_s^(i)dH_s^(i)在系数g满足Lipschitz条件,...本文讨论在金融中有重要应用价值的,由Lévy过程驱动的倒向双重随机微分方程: Y_t=ξ+∫_t^T f(s,Y_(s-),U_s,Z_s)ds+∫_t^T g(s,Y_(s-),U_s,Z_s)dB_s -∫_t^TU_sdW_s-sum for i=1 to ∞ Z_s^(i)dH_s^(i)在系数g满足Lipschitz条件,f满足推广的Bihari条件:|f(t,y_1,u_1,z_1)-f(t,y_2,u_2,z_2)|~2≤c(t)k(|y_1-y_2|~2)+K(|u_1-u_2|~2+||z_1-z_2||~2)时,利用推广It公式、Picard迭代法和区间延拓过程,证明了上述方程F_t适应解的存在唯一性,推广了其它文献以前的结论.展开更多
Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illust...Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illustrate the boundedness of solutions of a difference equation are also given.展开更多
文摘本文给出了Bihari不等式成在高维空间的一种推广形式。即证明了定理:设Ω_r表R^n中的球;S^2=sum from i=1 to n (S_i^2≤r^2),Q为R^n中有界可测集,u(s,x),f(s,x)为Ω_R×Q(R>r)下的非责有界连续函数,c≥0为常数,若 u(t,y≤c+∫f(s,x)φ[u(s,x)dxds] (1)对(t,y)∈Ω_r×Q(r<R)成立,其中φ(u)当0<u<ü(ü≤∞)为正的连续非减函数,又设ψ(u)=integral from n=0 to u du_1/(φu_1)(c<u<ü)这时如果 ∫Ω_r×Q~[f(s,x)dxds]<ψ(ü-0) (2)则有 supu(t,y)≤ψ^(-1)[f(s,x)dxds] (t,y)∈Ω_r×Q
文摘本文讨论在金融中有重要应用价值的,由Lévy过程驱动的倒向双重随机微分方程: Y_t=ξ+∫_t^T f(s,Y_(s-),U_s,Z_s)ds+∫_t^T g(s,Y_(s-),U_s,Z_s)dB_s -∫_t^TU_sdW_s-sum for i=1 to ∞ Z_s^(i)dH_s^(i)在系数g满足Lipschitz条件,f满足推广的Bihari条件:|f(t,y_1,u_1,z_1)-f(t,y_2,u_2,z_2)|~2≤c(t)k(|y_1-y_2|~2)+K(|u_1-u_2|~2+||z_1-z_2||~2)时,利用推广It公式、Picard迭代法和区间延拓过程,证明了上述方程F_t适应解的存在唯一性,推广了其它文献以前的结论.
基金Supported by the Program of Education Department of Sichuan Province(No.10ZA173)
文摘Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illustrate the boundedness of solutions of a difference equation are also given.
