Related papers: Jump Processes with Deterministic and Stochastic C…
In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…
Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuous dynamics, discrete transitions, or both, stochastic hybrid…
We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional and the rates are equal to the…
In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
This paper mainly investigates reflected stochastic recursive control problems governed by jump-diffusion dynamics. The system's state evolution is described by a stochastic differential equation driven by both Brownian motion and Poisson…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
We study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time…
We study the positive recurrence of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a…
This paper is devoted to studying an infinite time horizon stochastic recursive control problem with jumps, where infinite time horizon stochastic differential equation and backward stochastic differential equation with jumps describe the…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We allow the drift coefficient $b$ and the diffusion coefficient…
In this paper, we investigate the optimal control problems for stochastic differential equations (SDEs in short) of mean-field type with jump processes. The control variable is allowed to enter into both diffusion and jump terms. This…
The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Groups in ecology are often affected by sudden environmental perturbations. Parameters of stochastic models are often imprecise due to various uncertainties. In this paper, we formulate a stochastic Holling II one-predator two-prey system…