We present a method for learning latent stochastic differential equations (SDEs) from high dimensional time series data. Given high-dimensional generated lower unknown Itô process, the proposed learns mapping ambient to space, and underlying SDE coefficients, through self-supervised approach. Using framework of variational autoencoders, we consider conditional generative model data based on Eul...

In this article we address the stability of linear stochastic differential equations. particular, focus our attention on non-normality in Following Higham and Mao study a test problem for non-normal equations, that is stable without noise, prove property conjectured by Mao, an exponentially small (in dimension) noise term able to destabilise mean-square sense solution SDE.

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include correspondence weak solutions equations, well-posedness, regularity estimates, exponential ergodicity, long time large d...

One of the main tasks to analyze and design a mining system is predicting the behavior exhibited by prices in the future. In this paper, the applications of different prediction methods are evaluated in econometrics and financial management fields, such as ARIMA, TGARCH, and stochastic differential equations, for the time-series of monthly copper prices. Moreover, the performance of these metho...