Stochastic Process and Applications
نویسنده
چکیده
1.1 Probability Triple We introduce the probability triple (Ω,F , P ), which is the foundation of the probability analysis. Let Ω be a set and F be a collection of subsets of Ω. A point ω ∈ Ω ia a sample and A ∈ F is an event. The probability measure P assigns 0 ≤ P (A) ≤ 1 for each event A ∈ F , i.e. the probability of event A occurs: Definition The triple (Ω,F , P ) is the probability triple if (1) F is σ-algebra, i.e., Ω ∈ F , A ∈ F ⇒ Ac ∈ F Fn ∈ F ⇒ ⋃ n Fn ∈ F (2) P is σ-additive; for a sequence of disjoint events {An} in F ,
منابع مشابه
Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications
In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...
متن کاملBehavioral study of piston manufacturing plant through stochastic models
Piston plays a vital role in almost all types of vehicles. The present study discusses the behavioral study of a piston manufacturing plant. Manufacturing plants are complex repairable systems and therefore, it is difficult to evaluate the performance of a piston manufacturing plant using stochastic models. The stochastic model is an efficient performance evaluator for repairable systems. In...
متن کاملOptimal Stochastic Control in Continuous Time with Wiener Processes: General Results and Applications to Optimal Wildlife Management
We present a stochastic optimal control approach to wildlife management. The objective value is the present value of hunting and meat, reduced by the present value of the costs of plant damages and traffic accidents caused by the wildlife population. First, general optimal control functions and value functions are derived. Then, numerically specified optimal control functions and value func...
متن کاملApplications of TP2 Functions in Theory of Stochastic Orders: A Review of some Useful Results
In the literature on Statistical Reliability Theory and Stochastic Orders, several results based on theory of TP2/RR2 functions have been extensively used in establishing various properties. In this paper, we provide a review of some useful results in this direction and highlight connections between them.
متن کاملA New Hybrid Algorithm to Optimize Stochastic-fuzzy Capacitated Multi-Facility Location-allocation Problem
Facility location-allocation models are used in a widespread variety of applications to determine the number of required facility along with the relevant allocation process. In this paper, a new mathematical model for the capacitated multi-facility location-allocation problem with probabilistic customer's locations and fuzzy customer’s demands under the Hurwicz criterion is proposed. Thi...
متن کاملStochastic differential equations and integrating factor
The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.
متن کامل