Stochastic optimal control in infinite dimension
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 …
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …
[图书][B] Measure-Valued Branching Processes
Z Li, Z Li - 2011 - Springer
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 …
the law of chance. In this chapter we provide some basic characterizations and constructions …
Two-time-scale stochastic partial differential equations driven by -stable noises: Averaging principles
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 …
formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha …
[HTML][HTML] Derivative formulas and gradient estimates for SDEs driven by α-stable processes
X Zhang - Stochastic Processes and their Applications, 2013 - Elsevier
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 …
gradient estimate for stochastic differential equations driven by α-stable noises, where α∈(0 …
Cylindrical Lévy processes in Banach spaces
D Applebaum, M Riedle - Proceedings of the London …, 2010 - academic.oup.com
Cylindrical probability measures are finitely additive measures on Banach spaces that have
sigma-additive projections to Euclidean spaces of all dimensions. They are naturally …
sigma-additive projections to Euclidean spaces of all dimensions. They are naturally …
Ergodicity for functional stochastic differential equations and applications
In this paper, using the remote start or dissipative method, we investigate ergodicity for
several kinds of functional stochastic equations including functional stochastic differential …
several kinds of functional stochastic equations including functional stochastic differential …
Bismut formula for Lions derivative of distribution-path dependent SDEs
J Bao, P Ren, FY Wang - Journal of Differential Equations, 2021 - Elsevier
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 …
which varies as probability measure on the path space, we introduce the intrinsic and Lions …
[图书][B] The dynamics of nonlinear reaction-diffusion equations with small Lévy noise
A Debussche, M Högele, P Imkeller - 2013 - Springer
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 …
last decades in many areas of science extending from physics through chemistry and …
Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes
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) …
Burgers equations driven by α/2-subordinated cylindrical Brownian motions with α∈(1, 2) …
Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process
X Sun, L Xie, Y Xie - Bernoulli, 2022 - projecteuclid.org
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 …
driven by α-stable processes with slow and fast time-scales, where α∈(1, 2). We prove that …