Related papers: On the minimum exit rate for a diffusion process p…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
This paper proposes a distributionally robust approach to regret optimal control of discrete-time linear dynamical systems with quadratic costs subject to a stochastic additive disturbance on the state process. The underlying probability…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the…
In this paper, we consider an optimal control problem for a prescription opioid epidemic model that describes the interaction between the regular prescription or addictive use of opioid drugs, and the process of rehabilitation and that of…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We study the exit-time of a self-interacting diffusion from an open domain $G \subset \mathbb{R}^d$. In particular, we consider the equation $d{X_t} = - \left( \nabla V(X_t) + \frac{1}{t}\int_0^t\nabla F (X_t - X_s)d{s} \right) d{t} +…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
Jacobi diffusion is a representative diffusion process whose solution is bounded in a domain under certain drift and diffusion coefficient conditions. However, the process without such conditions has not been thoroughly investigated. We…
This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…
Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
The time needed for a particle to exit a confining domain through a small window, called the narrow escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean…
This article is about molecular simulation. However, the theoretical results apply for general overdamped Langevin dynamics simulations. Molecular simulation is often used for determining the stability of a complex (e.g., ligand-receptor).…
This study considers an optimal reinsurance, investment, and dividend strategy control problem for insurance companies in a regulated Markov regime-switching environment, intending to maximize long-run average reward. Unlike existing single…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process $Z_n$ with offspring distribution $Y$, there exists a random variable $X$…
I consider a stochastic optimization problem for a time-changed Bessel process whose diffusion rate is constrained to be between two positive values $r_{1}<r_{2}$. The problem is to find an optimal adapted strategy for the choice of…
This paper discusses the first exit and Dirichlet problems of the nonisotropic tempered $\alpha$-stable process $X_t$. The upper bounds of all moments of the first exit position $\left|X_{\tau_D}\right|$ and the first exit time $\tau_D$ are…