ﻻ يوجد ملخص باللغة العربية
We study convergence behaviors of degenerate and non-reversible stochastic differential equations. Our method follows a Lyapunov method in probability density space, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We construct a weighted Fisher information induced Gamma calculus method with a structure condition. Under this condition, an explicit algebraic tensor is derived to guarantee the convergence rate for the probability density function converging to its invariant distribution. We provide an analytical example for underdamped Langevin dynamics with variable diffusion coefficients.
We deal with the problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latters being characterized by degenerate d
We develop and analyze a method, density tracking by quadrature (DTQ), to compute the probability density function of the solution of a stochastic differential equation. The derivation of the method begins with the discretization in time of the stoch
The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established provided the
In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-peri
In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations in Hilbert