scholarly journals Skellam Type Processes of Order k and Beyond

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1193
Author(s):  
Neha Gupta ◽  
Arun Kumar ◽  
Nikolai Leonenko
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Stable Subordinator ◽  
Time Changes ◽  
Lévy Measures

In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Skellam process by independent stable subordinator and tempered stable subordinator, respectively. We derive the marginal probabilities, Lévy measures, governing difference-differential equations of the introduced processes. Our results generalize the Skellam process and running average of Poisson process in several directions.

scholarly journals On the Fractional Poisson Process and the Discretized Stable Subordinator

Axioms ◽  
2015 ◽  
Vol 4 (3) ◽  
pp. 321-344 ◽  
Author(s):  
Rudolf Gorenflo ◽  
Francesco Mainardi
Keyword(s):  
Poisson Process ◽  
Stable Subordinator ◽  
Fractional Poisson Process

scholarly journals NUMERICAL APPROACHES FOR A MATHEMATICAL MODEL OF AN FCCU REGENERATOR

2008 ◽  
Vol 7 (1) ◽  
pp. 71
Author(s):  
J. C. Penteado ◽  
C. O. R. Negrao ◽  
L. F. S. Rossi
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Difference Methods ◽  
Implicit Finite Difference ◽  
Conservation Principles ◽  
Continuously Stirred Tank Reactor ◽  
Time Changes ◽  
Numerical Approaches

This work discusses a mathematical model of an FCCU (Fluid Catalytic Cracking Unit) regenerator. The model assumes that the regenerator is divided into two regions: the freeboard and the dense bed. The latter is composed of a bubble phase and an emulsion phase. Both phases are modeled as a CSTR (Continuously Stirred Tank Reactor) in which ordinary differential equations are employed to represent the conservation of mass, energy and species. In the freeboard, the flow is considered to be onedimensional, and the conservation principles are represented by partial differential equations to describe space and time changes. The main aim ofthis work is to compare two numerical approaches for solving the set of partial and ordinary differential equations, namely, the fourth-order Runge-Kutta and implicit finite-difference methods. Although both methods give very similar results, the implicit finite-difference method can be much faster. Steady-state results were corroborated by experimental data, and the dynamic results were compared with those in the literature (Han and Chung, 2001b). Finally, an analysis of the model’s sensitivity to the boundary conditions was conducted.

Formation of non-Gaussian random processes, signals and interference, on the basis of stochastic differential equations

2018 ◽  
pp. 45-58
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Stochastic Differential Equations ◽  
Gaussian Processes ◽  
Random Processes ◽  
Parametric Noise ◽  
Non Gaussian

Reviewed and analyzed issues associated with the formation of naguszewski random processes using stochastic differential equations. Algorithms of formation of scalar, vector and n –connected continuous Markov non-Gaussian sequences are considered. Forming filters with parametric noise and with disturbing influences, which are not Gaussian processes, are analyzed. The analysis of formation of non Gaussian sequences by means of Poisson process and stochastic filters is carried out.

scholarly journals Ruin Probability in Compound Poisson Process with Investment

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Yong Wu ◽  
Xiang Hu
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Ruin Probability ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Compound Poisson ◽  
Risky Assets ◽  
Black Scholes Model ◽  
Black Scholes

We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.

scholarly journals FRACTIONAL PROCESSES: FROM POISSON TO BRANCHING ONE

2008 ◽  
Vol 18 (09) ◽  
pp. 2717-2725 ◽  
Author(s):  
V. V. UCHAIKIN ◽  
D. O. CAHOY ◽  
R. T. SIBATOV
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Poisson Process ◽  
Fractional Differential Equations ◽  
Waiting Times ◽  
Numerical Calculations ◽  
Monte Carlo Algorithm ◽  
Limit Distributions ◽  
Fractional Differential

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Lèvy stable densities are discussed and used for the construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distributions of the normalized variable Z = N/〈N〉 are found for both processes.

scholarly journals A system of functional-differential equations associated with the optimal detection problem for jump-times of a Poisson process

1998 ◽  
Vol 11 (2) ◽  
pp. 179-192 ◽  
Author(s):  
Doncho S. Donchev
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Existence And Uniqueness ◽  
Value Function ◽  
Functional Differential Equations ◽  
Optimal Detection ◽  
Detection Problem ◽  
Special System ◽  
Functional Differential ◽  
The Value Function

The value function in the optimal detection problem for jump-times of a Poisson process satisfies a special system of functional-differential equations. In this paper, we investigate the system and prove the existence and uniqueness of its solution.

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