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1.
AsymptoticFormulaforProbabilisticRepresentationsof(C_0)OperatorSemigroups¥ChenWenzhong(陈文忠)(DepartmentofMathematics,XiamenUni?..  相似文献
2.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS   总被引:1,自引:0,他引:1       下载免费PDF全文
§1.IntroductionLet(?,F)be a measurable space and let Lb(F)be the space of F-measurable andbounded real functions.A nonlinear expectation is a continuous functionalE[·]:Lb(F)?→Rthat is order preserving(i.e.,E[X1]≥E[X2],if X1≥X2)and constant preserving  相似文献
3.
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs. The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.  相似文献
4.
The probabilistic approach is used for constructing special layer methods to solve the Cauchy problem for semilinear parabolic equations with small parameter. Despite their probabilistic nature these methods are nevertheless deterministic. The algorithms are tested by simulating the Burgers equation with small viscosity and the generalized KPP-equation with a small parameter.

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5.
A number of new layer methods for solving the Neumann problemfor semilinear parabolic equations are constructed by usingprobabilistic representations of their solutions. The methodsexploit the ideas of weak-sense numerical integration of stochasticdifferential equations in a bounded domain. In spite of theprobabilistic nature these methods are nevertheless deterministic.Some convergence theorems are proved. Numerical tests on theBurgers equation are presented.  相似文献
6.
A number of new layer methods for solving the Dirichlet problemfor semilinear parabolic equations are constructed by usingprobabilistic representations of their solutions. The methodsexploit the ideas of weak sense numerical integration of stochasticdifferential equations in a bounded domain. Despite their probabilisticnature these methods are nevertheless deterministic. Some convergencetheorems are proved. Numerical tests are presented.  相似文献
7.
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.  相似文献
8.
SO. IntroductionPeng[1] introduced the notions of g--expectation and conditional g--expectation as wellas g-maltingale illtroduced via BSDEs, he proved that under suitable square integrabiLity assumption on coefficient g and terminal value (, the g--expectation and conditionalg-expectation of the random variable (preserve many of the basic properties (except linearity) of the convenient mathematical expectation and conditional expectation. More recelltly, under the assumption of continuous p…  相似文献
9.
In this paper,we investigate the problem:How big are the increments of G-Brownian motion.We obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian motion.As applications of this result,we get the law of iterated logarithm and the Erds and R′enyi law of large numbers for G-Brownian motion.Furthermore,it turns out that our theorems are natural extensions of the classical results obtained by Csrg and R′ev′esz(1979).  相似文献
10.
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