the control problem and dynamic programming is a powerful tool in economics and management. we review the dynamic programming problem from its beginning up to its present stages. a problem which was involved in physics and mathematics in i 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Itô formula for Hurst parameter bigger than 1 2 .

We present stochastic process algebra models of a Circadian clock mechanism used in many biological organisms to regulate time-based behaviour. We compare modelling techniques from different modelling paradigms, PEPA and stochastic π-calculus.

Preface The importance of the martingale concept cannot be overemphasized. .. . ] Martingales, Markov dependence and stationarity are the only three dependence concepts so far isolated which are suuciently general and suuciently amenable to investigation yet with a great number of deep properties. This project report deals with the stochastic calculus of semimartingales. In Doob's classical boo...

Using time-reversal, we introduce the stochastic integration for zero-energy additive functionals of symmetric Markov processes, which extends an early work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained. AMS 2000 Mathematics Subject Classification: Primary 31C25; Secondary 60J57, 60J55, 60H05.

We study the stochastic integral defined by Skorohod in [24] of a possibly anticipating integrand, as a function of its upper limit, and establish an extended It6 formula. We also introduce an extension of Stratonovich's integral, and establish the associated chain rule. In all the results, the adaptedness of the integrand is replaced by a certain smoothness requirement.

• Ω: An abstract space of points ω ∈ Ω. • F : a σ-field (or σ-algebra) on Ω. That is, a collection of subsets of Ω satisfying: 1. Ω ∈ F . 2. Let A ⊆ Ω such that A ∈ F then Ac = Ω−A ∈ F . 3. Let A1, A2, A3, · · · ∈ F then A1 ∪A2 ∪A3 ∪ · · · ∈ F . The elements of F are called events. Condition (1) above simply states that the space Ω is necessarily an event. Conditions (2) and (3) state that the ...

In this paper we extend the recent work of C.A. Braumann [1] to the case of stochastic differential equation with random coefficients. Furthermore, the relationship of the Itô-Stratonovich stochastic calculus to studies of random population growth is also explained.

In this paper we propose a stochastic broadcast π-calculus which can be used to model server-client based systems where synchronization is always governed by only one participant. Therefore, there is no need to determine the joint synchronization rates. We also take immediate transitions into account which is useful to model behaviors with no impact on the temporal properties of a system. Since...

This is a brief tutorial on how to do informal stochastic calculus and why it works. I state all the theoretical results needed to compute, I properly compute solutions to two famous SDEs, and I show you how to get the same answers by manipulating Leibniz notation. Then I shows how the Leibniz notation relates to all those theoretical results (there is a neat sort of “lexical isomorphism”). Fin...