A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Forward-backward热方程差分逼近的直接算法

通过利用区域分解技术和并行算法的思想 ,把原问题分解为几个完全独立的子区域上的问题 ,并直接并行求解 ,然后把这些解作适当的线性组合 ,得到原问题的解 .给出了 Forward-

Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward-backward method

This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME

The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.

Solutions to general forward-backward doubly stochastic differential equations

A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus

This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.

求解双层凸优化问题的Forward-Backward分裂算法

Forward-Backward分裂算法是求解极大单调算子和问题以及极小化具有可分结构的凸函数和问题的有效算法。本文利用该算法在Hilbert空间中构造出了求解双层优化问题的分裂算法。与已有文献相比,所提算法不仅在参数的选取上更加灵活,而且本文还证明了该算法生成的点列能收敛到双层优化问题的解。

Iterative methods for a forward-backward heat equation in two-dimension

A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.

Parton Rescattering Effect on the Charged Hadron Forward-Backward Multiplicity Correlation in pp Collisions at s～(1/2)=200 GeV

The parton rescattering effect on the charged hadron forward-backward multiplicity correlation in pp collisions at √s =200 GeV is studied by a parton and hadron cascade model, PACIAE, based on the PYTHIA model. The calculated multiplicity and pseudorapidity distribution of the final state charged hadrons are well compared with the experimental data. It is found that the final state charged hadron pseudorapidity distribution is different from the initial state charged partons. The parton rescattering effect on the charged hadron forward-backward multiplicity correlation increases with the increasing parton rescattering strength in the center pseudorapidity region （｜η｜ 〈 1）. However, this effect becomes weaker in the outer pseudorapidity region （｜η｜ 〉 1）.

GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.

Non-Markovian Forward-Backward Stochastic Differential Equations with Discontinuous Coefficients

In this paper, the existence and uniqueness of a weak solution in the sense of [1] and [2] has been shown for a class of fully coupled forward-backward SDE (FBSDE) such that the forward drift coefficient is allowed to be discontinuous with respect to the backward component of the solution. The novelty of this paper lies on the fact that the FBSDE is non-Markovian, i.e., the coefficients of the FBSDEs are allowed to be random. This type of FBSDEs is inspired by the regime shift model, where the short term interest rate switches between regimes according to the rate level. As a consequence, the discontinuity of the system becomes inevitable, making it violate the usual assumptions of most existing results for FBSDEs. We show the weak well-posedness of the FBSDE by an approximation scheme, along with the decoupling strategy.

带驻留时间HMM2的Forward-Backward算法

讨论了用状态驻留时间来模型化传统HMM2模型,对传统HMM2的状态转移和输出观测值的Markov假设条件作了改进,在新模型的转移概率和输出观测值的概率中加入驻留时间,并在传统HMM2的基础上定义了新模型的前向-后向变量算法,导出了新模型的前向-后向算法的迭代公式,以及在给定模型λ的条件下,产生观测序列O的概率计算公式.

The Maximum Principle for Fully Coupled Forward-backward Stochastic Control System

The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.

Forward-backward multiplicity correlations 4.5 A GeV/c ^16O-emulsion interactions

A detailed study of the mechanisms of the emissions of pions and protons in the forward and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has been carried out. The correlations between the multiplicities of secondary charged particles in the backward and forward hemispheres are investigated.

Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems

This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward-forward systems of equations of mean field games. We present local well-posedness, global existence and some regularity results for these equations.

Existence of Solutions for Forward-Backward Stochastic Differential Equations with Jumps and Non-Lipschitzian Coefficients

This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.

MAXIMUM PRINCIPLE FOR OPTIMAL CONTROLPROBLEM OF FULLY COUPLEDFORWARD-BACKWARD STOCHASTIC SYSTEMS

The optimal control problem of fully coupled forward-backward stochastic systems is put forward. A necessary condition, called maximum principle, for an optimal control of the problem with the control domain being convex is proved.

MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROL SYSTEM WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE

Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both diffusion and jump coefficients.The result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization problem.Explicit expressionof the optimal portfolio selection strategy is obtained in the state feedback form.

Forward-backward doubly stochastic differential equations and related stochastic partial differential equations

The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations （FBDSDEs）. It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistie interpretation for the solutions to a class of quasilinear stochastic partial differential equations （SPDEs） combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backvzard variable.

An ocean circulation model based on Eulerian forward-backward difference scheme and three-dimensional, primitive equations and its application in regional simulations

A two-time-level, three-dimensional numerical ocean circulation model is established with a two-level, single-step Eulerian time-difference scheme. The mathematical model of the large-scale oceanic motions is based on the terrain-following coo-rdinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-back-ward method is adopted to replace the most preferred leapfrog scheme as the time-difference method for both barotropic and barocli-nic modes. The forward-backward method is of the second order of accuracy, requires only once of the function evaluation per time step, and is free of the computational mode inherent in the three-level schemes. It is superior in many respects to the original leapfrog and Asselin-filtered leapfrog schemes in the practical use. The performance of the newly-built circulation model is tested by simula-ting a barotropic （tides in marginal seas of China） and a baroclinic phenomenon （seasonal evolution of the Yellow Sea Cold Water Mass）, respectively. The three-year time histories of four prognostic variables obtained by the POM model and the two-time-level model are compared in a regional simulation experiment for the northwest Pacific to further show the reliability of the two-level scheme circulation model.