In various fields, such as teletraffic and economics, measured times series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a non-stationary process. To overcome this problem we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a...

This chapter focuses on stochastic control and decision processes that occur in a variety of theoretical and applied contexts, such as statistical decision problems, stochastic dynamic programming problems, gambling processes, optimal stopping problems, stochastic adaptive control processes, and so on. It has long been recognized that these are all mathematically closely related. That being the...

Gaussian process modeling (also known as kriging) is an empirical modeling approach that has been widely applied in engineering for the approximation of deterministic functions, due to its flexibility and ability to interpolate observed data. Despite its statistical properties, Gaussian process models (GPM) have not been employed to describe the dynamics of stochastic systems with multiple outp...

We consider the problem of routing incoming airplanes to two runways of an airport. Due to air turbulence, the necessary separation time between two successive landing operations depends on the types of the airplanes. When viewed as a queuing problem, this means that we have dependent service times. The aim is to minimize waiting times of aircrafts. We consider here a model where arrivals form ...

One of the actions usually conducted to limit exposure a hazardous event is evacuation area that subject effects itself. This involves modifications both demand (a large number users all want move together) and supply (the transport network may experience changes in capacity, unusable roads, etc.). In order forecast traffic evolution during an evacuation, natural choice adopt approach based on ...

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are that they measure risk of processes that are functions of the history of the base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property....

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

This paper describes a novel approach to both learning and computing Nash equilibrium in continuous games that is especially useful for analyzing structural game theoretic models of imperfect competition and oligopoly. We depart from the methods and assumptions of the traditional “Calculus” approach to computing equilibrium. Instead, we use a new and natural interpretation of games as condition...

Abstract In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup and configuration selection are considered simultaneously. More precisely, works under set configurations requires times to switch from one another. Also, time job is function its position configuration. The objective find sequence...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...