It is known that optimal stopping problems form an important class of optimal control problems having applications in stochastic calculus (maximal inequalities), statistics (sequential analysis) and mathematical finance (American options). The results about the relationship between optimal stopping problems for Markov processes and free-boundary problems for partial differential equations often...

An effective macroscopic model for a stochastic microscopic system is derived. The original microscopic system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes or heterogeneities. The homogenized effective model is still a stochastic partial differential equation but defined on a unified domain without holes. The solutions of the microscop...

This paper presents a stochastic formulation of a class of identification problems for partial differential equations, known as 'inverse' problems in the mathematicalphysics literature. By introducing stochastic processes to model errors in observation as well as 'disturbance' we can provide a precise formulation to interpret what appear to be 'ad hoc' techniques, especially in the treatment of...

this paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. in the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). however,, two significant criteria for each schedule in stochastic models are: expectable m...

Performance evaluation of electricity distribution units is an important issue between researchers and regulators. Classic Data Envelopment Analysis models with deterministic data have been used by many authors to measure efficiency of power distribution units in different countries. However, Data Envelopment Analysis with stochastic data are rarely used to measure efficiency of distribution co...

In this paper we use a stochastic differential equation to describe the dynamic evolution of the height of an individual tree. The first model is defined by Gompertz shape stochastic differential equation. The second model is defined by Gompertz stochastic differential equation with a threshold parameter. This model can be considered as an extension of the three parameter stochastic Gompertz mo...

In this research, Allan Variance analysis is used to identify the stochastic error sources existing in inertial sensors and to determine the corresponding noise parameters. According to the noise parameters, the power spectral density (PSD) function of the stochastic error sources can be determined. The differential equation descriptions for individual stochastic errors are then derived for two...

Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as cluster coefficient often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we study the problem of enforcing edge differential privacy in graph generation. The idea is to enfo...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...

We introduce a spatial extension of stochastic π-calculus that provides a formalism to model systems of discrete, connected locations. We define the extended stochastic semantics and also give deterministic semantics in terms of a system of ordinary differential equations. We describe two simple examples, one based on a standard epidemic model and one modelling resistance in plant tissues.