The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

A measure-valued process describes the evolution of a population that evolves according to
the law of chance. In this chapter we provide some basic characterizations and constructions …

This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale
formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha …

In this paper we prove a derivative formula of Bismut–Elworthy–Li's type as well as a
gradient estimate for stochastic differential equations driven by α-stable noises, where α∈(0 …

Cylindrical probability measures are finitely additive measures on Banach spaces that have
sigma-additive projections to Euclidean spaces of all dimensions. They are naturally …

In this paper, using the remote start or dissipative method, we investigate ergodicity for
several kinds of functional stochastic equations including functional stochastic differential …

To characterize the regularity of distribution-path dependent SDEs in the initial distribution
which varies as probability measure on the path space, we introduce the intrinsic and Lions …

Dynamical systems perturbed by small random noise have received a vast attention over the
last decades in many areas of science extending from physics through chemistry and …

In this work, we prove the strong Feller property and the exponential ergodicity of stochastic
Burgers equations driven by α/2-subordinated cylindrical Brownian motions with α∈(1, 2) …

In this paper, we study the averaging principle for a class of stochastic differential equations
driven by α-stable processes with slow and fast time-scales, where α∈(1, 2). We prove that …