We investigate the optimal control problems for backward doubly stochastic control systems.
As a necessary condition of the optimal control we obtain a stochastic maximum principle. …

We study the existence of quasi-periodic, invariant tori in a nearly integrable Hamiltonian
system of high order proper degeneracy, ie, the integrable part of the Hamiltonian involves …

We study the persistence of lower-dimensional tori in Hamiltonian systems of the form H(x,y,z)=〈ω,y〉+12〈z,M(ω)z〉+εP(x,y,z,ω),
where (x,y,z)∈T n ×R n ×R 2m , ε is a small parameter, …

In this paper, the existence of periodic solutions of Fokker–Planck equations is obtained by
discussing the existence of periodic solutions in distribution for some stochastic differential …

We obtain a maximum principle for stochastic control problem of general controlled stochastic
differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This …

This paper proposes a deep learning approach for solving optimal stopping problems and
high-dimensional American-style options pricing problems. Through state-space partition, the …

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic
differential equations. The estimates, based on either the continuously observed process …

In this paper, we study the stochastic optimal control problem for control systems with time-varying
delay. The corresponding state equation is a kind of stochastic differential delay …

In this paper, we discuss the dynamics of a stochastic SIQS epidemic model. When the
noise is large, the infective decays exponentially to zero regardless of the magnitude of R 0 . …

We propose a modified least squares estimator for the drift parameter of the Ornstein–Uhlenbeck
process when the observations are available at a discrete instant in a low-frequency …