随机系数跳扩散系统带不定权重的递归随机线性二次控制
Recursive Stochastic Linear-Quadratic Control with Indefinite Weights for Jump-Diffusion Systems with Random Coefficients
浏览论文内容
中文总结 AI 辅助
针对带随机系数的跳扩散系统，研究不定权重下的递归随机LQ控制，通过测度变换和配方法推导随机Riccati方程，并给出反馈最优性与唯一性条件。
中文摘要 AI 辅助
我们研究具有有界随机系数、不定权重和线性递归成本的有限活动跳扩散的有限时域随机线性二次（LQ）控制问题。该成本由后向随机微分方程（BSDE）定义，其生成元具有乘以布朗运动和跳跃被积函数的有界确定性系数。通过布朗-泊松测度变换和一个积分因子，将准则简化为非递归的LQ泛函。在物理空间和变换后的平方可积控制空间的交集上，我们建立了在变换测度下L^1二次数据的递归评估，并证明了其与完整变换值的相等性。在变换后的均匀凸性和无控制跳跃映射的可逆性条件下，我们从非递归值核中识别出随机Riccati方程。条件能量估计证明了将其鞅系数转移到物理测度的合理性。通过配方法，我们得到了反馈表示、比较性和反馈可容许类中的唯一性。对于每个初始对，当变换后的优化器具有有限的物理控制能量时，递归值恰好达到。分析实例展示了具有负控制权重的非零反馈和均匀凸性。
英文摘要
We study finite-horizon stochastic linear-quadratic (LQ) control for finite-activity jump diffusions with bounded random coefficients, indefinite weights and a linear recursive cost. The cost is defined by a backward stochastic differential equation (BSDE) whose generator has bounded deterministic coefficients multiplying the Brownian and jump integrands. A Brownian-Poisson change of measure and an integrating factor reduce the criterion to a nonrecursive LQ functional. On the intersection of the physical and transformed square-integrable control spaces, we establish recursive evaluation for L^1 quadratic data under the transformed measure and equality with the full transformed value. Under transformed uniform convexity and invertibility of the uncontrolled jump map, we identify the stochastic Riccati equation from the nonrecursive value kernel. Conditional energy estimates justify transferring its martingale coefficients to the physical measure. Completion of squares gives feedback representation, comparison and uniqueness in the feedback-admissible class. For each initial pair, the recursive value is attained exactly when the transformed optimizer has finite physical control energy. Analytical examples illustrate nonzero feedback and uniform convexity with a negative control weight.
