Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of divisio...Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.展开更多
A class of stochastic differential equations(SDEs) driven by semimartingale with non-Lipschitz coefficients was studied.By using Gronwall inequality,the non-confluence of solutions is proved under the general conditions.
Via a forward SDE solution(k_(t),t≥O)that captures money supply dynamics,a macroeconomic model known as the monetary model generates a backward exchange rate process(y_(t),t≥0).For any t≥0,y_(t)=k_(t)+α^(-1)μ_(t)...Via a forward SDE solution(k_(t),t≥O)that captures money supply dynamics,a macroeconomic model known as the monetary model generates a backward exchange rate process(y_(t),t≥0).For any t≥0,y_(t)=k_(t)+α^(-1)μ_(t) where(μ_(t),t≥0)is a backward process andα>0 is a constant.Thus,(y_(t),t≥O)does not satisfy a conventional BSDE.Our paper proves(y_(t),t≥O)is a continuous semimartingale when restrictions on the SDE for(k_(t),t≥O)capture anti-inflationary initiatives.This new result in economic dynamics does not require the filtration to be the Brownian filtration.展开更多
文摘Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.
基金National Natural Science Foundation of China(No.71171003)Natural Science Foundation of Anhui Province of China(No.090416225)Natural Science Foundation of Universities of Anhui Province of China(No.KJ2010A037)
文摘A class of stochastic differential equations(SDEs) driven by semimartingale with non-Lipschitz coefficients was studied.By using Gronwall inequality,the non-confluence of solutions is proved under the general conditions.
文摘Via a forward SDE solution(k_(t),t≥O)that captures money supply dynamics,a macroeconomic model known as the monetary model generates a backward exchange rate process(y_(t),t≥0).For any t≥0,y_(t)=k_(t)+α^(-1)μ_(t) where(μ_(t),t≥0)is a backward process andα>0 is a constant.Thus,(y_(t),t≥O)does not satisfy a conventional BSDE.Our paper proves(y_(t),t≥O)is a continuous semimartingale when restrictions on the SDE for(k_(t),t≥O)capture anti-inflationary initiatives.This new result in economic dynamics does not require the filtration to be the Brownian filtration.
基金Supported by National Basic Research Program of China(973 Program2007CB814901)+1 种基金National Natural Science Foundation of China(10826098)Anhui Natural Science Foundation (090416225)
