Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the...Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations （SPDIEs） is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.展开更多
This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tail...This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n ≥ 0} is a binomial process with a parameter p ∈ (0,1) and independent of {Xn,n ≥ 1}; {M(n),n ≥ 0} is a Poisson process with intensity λ > 0, Sn = ΣNn i=1 Xi-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10771122,11071145)the Shandong Provincial Natural Science Foundation of China (No. Y2006A08)+2 种基金the Foundation for Innovative Research Groups of National Natural Science Foundation of China (No. 10921101)the National Basic Research Program of China (the 973 Program) (No. 2007CB814900)the Independent Innovation Foundation of Shandong University (No. 2010JQ010)
文摘Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations （SPDIEs） is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.
文摘This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n ≥ 0} is a binomial process with a parameter p ∈ (0,1) and independent of {Xn,n ≥ 1}; {M(n),n ≥ 0} is a Poisson process with intensity λ > 0, Sn = ΣNn i=1 Xi-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.
