Using Fractional Brownian motion with Machine Learning part12 | by Monodeep Mukherjee | Sep, 2023
- The World Most Precept for Optimum Management of Partially Noticed Stochastic Techniques Pushed by Fractional Brownian Movement(arXiv)
Writer : Yueyang Zheng, Yaozhong Hu
Summary : On this paper we research the stochastic management downside of partially noticed (multi-dimensional) stochastic system pushed by each Brownian motions and fractional Brownian motions. Within the absence of the highly effective instrument of Girsanov transformation, we introduce and research new stochastic processes that are used to rework the unique downside to a “classical one”. The adjoint backward stochastic differential equations and the required situation happy by the optimum management (most precept) are obtained
2. Giant deviations of slow-fast methods pushed by fractional Brownian movement(arXiv)
Writer : Siragan Gailus, Ioannis Gasteratos
Summary : We contemplate a multiscale system of stochastic differential equations wherein the sluggish part is perturbed by a small fractional Brownian movement with Hurst index H>1/2 and the quick part is pushed by an impartial Brownian movement. Working within the framework of Younger integration, we use instruments from fractional calculus and weak convergence arguments to determine a Giant Deviation Precept within the homogenized restrict, because the noise depth and time-scale separation parameters vanish at an acceptable charge. Our method relies within the research of the limiting conduct of an related managed system. We present that, in sure instances, the non-local charge operate admits an specific non-variational kind. The latter permits us to attract comparisons to the case H=1/2 which corresponds to the classical Freidlin-Wentzell principle. Furthermore, we research the asymptotics of the speed operate as H→1/2+ and present that it’s discontinuous at H=1/2
