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.

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.

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-

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。

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.

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 method of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.

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～(1/2)=200 GeV is studied by a parton and hadron cascade model,PACIAE,based on the PYTHIA model.The calculated multiplicity and pseudorapidity distri-bution 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).

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.

Distributed regularized online optimization using forward-backward splitting

This paper considers the problem of distributed online regularized optimization over a network that consists of multiple interacting nodes.Each node is endowed with a sequence of loss functions that are time-varying and a regularization function that is fixed over time.A distributed forward-backward splitting algorithm is proposed for solving this problem and both fixed and adaptive learning rates are adopted.For both cases,we show that the regret upper bounds scale as O(VT),where T is the time horizon.In particular,those rates match the centralized counterpart.Finally,we show the effectiveness of the proposed algorithms over an online distributed regularized linear regression problem.

L^(p)-Estimate for Linear Forward-Backward Stochastic Differential Equations

This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we obtain an L^(P)-result(p>2),including the existence and uniqueness of the p-th power integrable solution,a p-th power estimate,and a related continuous dependence property of the solution on the coefficients,for coupled linear FBSDEs in the monotonicity framework over large time intervals.In order to get rid of the stubborn constraint commonly existing in the literature,i.e.,the Lipschitz constant of σ with respect to z is very small,we introduce a linear transformation to overcome the difficulty on small intervals,and then"splice"the L^(P)-results obtained on many small intervals to yield the desired one on a large interval.

基于格密码的5G-R车地认证密钥协商方案

5G-R作为我国下一代高速铁路无线通信系统,其安全性对于保障行车安全至关重要。针对5G-AKA协议存在隐私泄露、根密钥不变和效率低等问题,基于格密码理论提出一种新型5G-R车地认证方案。首先,使用临时身份信息GUTI代替SUCI,克服了SUCI明文传输的缺点。其次,设计基于格密码的根密钥更新策略,采用格上公钥密码体制、近似平滑投射散列函数和密钥共识算法,实现了根密钥的动态更新和前后向安全性。再次,加入随机质询和消息认证码,实现了通信三方的相互认证,可有效防范重放、DoS等多种恶意攻击。最后,采用串空间形式化方法进行安全验证,结果表明:本文方法较其他方法有更高的安全性,被攻击成功的概率最低,仅为O(n^(2))×2^(-128),且有较低的计算开销和通信开销,能够满足5G-R高安全性的需求。

一种求解包含问题的算法研究

一种实希尔伯特空间中求解包含问题的算法被提出,所提出的算法基于向前向后方法、压缩方法、惯性方法和无需搜索的自适应步长。算法的特点为迭代中多次使用惯性加速方法,且自适应步长随着迭代次数增加可能增大。在包含问题解集非空、一个映射极大单调、另一个映射单调且利普希茨连续的假设下,算法的强收敛性被证明。

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.