The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a loca...The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a localization argument,we obtain the bicontinuous modification of local time.Furthermore,we give the Tanaka formula for convex functions of G-martingales.展开更多
We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),...We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.展开更多
In this paper, Tanaka formulae for (α, d,β)-superprocesses in the dimensions where the local time exists are established under the optimal initial condition.
Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0...Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0,∞),.x∈R.另一种是由游程理论定义的局部时lt(x),并给出这两种局部时之间的关系Lt(0)=24lt(0).展开更多
In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding solution.Furthermore,we are able to obtain explici...In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding solution.Furthermore,we are able to obtain explicit solutions to an interesting class of nonlinear BSDEs,including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing.Moreover,we show its applications in PDEs and contingent pricing in an incomplete market.展开更多
基金Supported by the National Natural Science Foundation of China(No.11601282)the Natural Science Foundation of Shandong Province(No.ZR2016AQ10)
文摘The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a localization argument,we obtain the bicontinuous modification of local time.Furthermore,we give the Tanaka formula for convex functions of G-martingales.
基金Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Department of Mathematics at the University of Oregon。
文摘We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.
基金supported in part by the National Natural Science Foundation of China(Grant No.10101002).
文摘In this paper, Tanaka formulae for (α, d,β)-superprocesses in the dimensions where the local time exists are established under the optimal initial condition.
文摘Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0,∞),.x∈R.另一种是由游程理论定义的局部时lt(x),并给出这两种局部时之间的关系Lt(0)=24lt(0).
基金This paper was originally exhibited in 2020(arXiv:2006.00222)。
文摘In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding solution.Furthermore,we are able to obtain explicit solutions to an interesting class of nonlinear BSDEs,including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing.Moreover,we show its applications in PDEs and contingent pricing in an incomplete market.
