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Jiong-min Yong 《高校应用数学学报(英文版)》2013,28(4):383-394
In this paper, we present a brief survey on the updated theory of backward stochas-tic Volterra integral equations (BSVIEs, for short). BSVIEs are a natural generalization of backward stochastic diff erential equations (BSDEs, for short). Some interesting motivations of studying BSVIEs are recalled. With proper solution concepts, it is possible to establish the corresponding well-posedness for BSVIEs. We also survey various comparison theorems for solutions to BSVIEs. 相似文献
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Jiongmin Yong 《Applicable analysis》2013,92(11):1429-1442
Continuous-time dynamic convex and coherent risk measures are introduced. To obtain existence of such risk measures, backward stochastic Volterra integral equations (BSVIEs, for short) are studied. For such equations, notion of adapted M-solution is introduced, well-posedness is established, duality principles and comparison theorems are presented. Then a class of dynamic convex and coherent risk measures are identified as a component of the adapted M-solutions to certain BSVIEs. 相似文献
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In this paper, we study a class of Hilbert space-valued forward-backward stochastic differential equations (FBSDEs) with bounded random terminal times; more precisely, the FBSDEs are driven by a cylindrical Brownian motion on a separable Hilbert space and a Poisson random measure. In the case where the coefficients are continuous but not Lipschitz continuous, we prove the existence and uniqueness of adapted solutions to such FBSDEs under assumptions of weak monotonicity and linear growth on the coefficients. Existence is shown by applying a finite-dimensional approximation technique and the weak convergence theory. We also use these results to solve some special types of optimal stochastic control problems. 相似文献
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DISCRETIZATION OF JUMP STOCHASTIC DIFFERENTIAL EQUATIONS IN TERMS OF MULTIPLE STOCHASTIC INTEGRALS 总被引:1,自引:0,他引:1
1.IntroductionFOrthestrongdiscretizationofSDEs,anynumericalmethodwhichonlydependsonthevaluesofBrownianpathsorPoissonpathsatthepartitionnodescannotachieveanorderhigherthan0.5ingeneral[')'1'].Thereforetheevaluationofmultiplestochasticintegralsontheintervalsbetweennodesisamajorobstaclethatmustbeovercome.Someattemptshavebeenmadepreviouslyindifferentapproachestoapproximatemul-tiplestochasticintegrals.[2]suggestsanapproximationintermsofFourierGaussiancoefficientsoftheBrownianbridgeprocess.Asthel… 相似文献
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We prove the Hölder continuity of some stochastic Volterra integrals, with singular kernels, under integrability assumptions on the integrand. Some applications to processes arising in the analysis of the fractional Brownian motion are given. The main tool is the embedding of some Besov spaces into some sets of Hölder continuous functions. 相似文献
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??In this paper, we study a class of stochastic Volterra equations, which include the stochastic differential equation driven by fractional Brownian motion. By using a maximal inequality due to It\^o (1979), we establish the central limit theorem for stochastic Volterra equation on the continuous path space, with respect to the uniform norm. 相似文献
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An invariance principle for semimartingale reflecting Brownian motions in an orthant 总被引:1,自引:0,他引:1
Semimartingale reflecting Brownian motions in an orthant (SRBMs) are of interest in applied probability because of their role
as heavy traffic approximations for open queueing networks. It is shown in this paper that a process which satisfies the definition
of an SRBM, except that small random perturbations in the defining conditions are allowed, is close in distribution to an
SRBM. This perturbation result is called an invariance principle by analogy with the invariance principle of Stroock and Varadhan
for diffusions with boundary conditions. A crucial ingredient in the proof of this result is an oscillation inequality for
solutions of a perturbed Skorokhod problem. In a subsequent paper, the invariance principle is used to give general conditions
under which a heavy traffic limit theorem holds for open multiclass queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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In this article, we consider a complex-valued and a measure-valued measure on , the space of all real-valued continuous functions on . Using these concepts, we establish the measure-valued Feynman-Kac formula and we prove that this formula satisfies a Volterra integral equation. The work here is patterned to some extent on earlier works by Kluvanek in 1983 and by Lapidus in 1987, but the present setting requires a number of new concepts and results.
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RBSDE''''s with jumps and the related obstacle problems for integral-partial differential equations 总被引:2,自引:0,他引:2
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation. 相似文献
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Shao Lin JI Zhen WU 《数学学报(英文版)》2007,23(12):2189-2204
The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk. The dynamic measure of risk to an investor in a financial market can be studied in our framework where the wealth equation may have nonlinear coefficients. 相似文献
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BO LiJun SHI KeHua & WANG YongJin Department of Mathematics Xidian University Xi’an China School of Mathematical Sciences Nankai University Tianjin China 《中国科学A辑(英文版)》2009,52(5):895-907
In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations
driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Galerkin scheme to approximate the solutions.
This work was supported by the LPMC at Nankai University and National Natural Science Foundation of China (Grant No. 10671036) 相似文献
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讨论了一类带分数Brown运动时变随机种群收获系统数值解的均方散逸性.在一定条件下,利用It公式和Bellman-Gronwall-Type引理,研究了方程(1)具有均方散逸性.分别利用带补偿的倒向Euler方法和分步倒向Euler方法讨论数值解的均方散逸性存在的充分条件,并通过数值算例对所给出的结论进行了验证. 相似文献