On the theory of differential equations of random processes. I, II

1955 ◽  
pp. 111-161 ◽  
Author(s):  
I. I. Gihman
Keyword(s):  
Differential Equations ◽  
Random Processes

scholarly journals MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA

2019 ◽  
Vol 5 (4) ◽  
pp. 0392-0402
Author(s):  
Matheus Dias Carvalho ◽  
Ricardo de Carvalho Falcão ◽  
Antonio Marcos de Oliveira Siqueira
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Metabolic Rate ◽  
Stationary State ◽  
Analytical Solutions ◽  
Random Processes ◽  
Graphical Form ◽  
Partial Differential

This article has elucidated information about Brownian Motion in the ring, something that is still little explored in the literature. In addition, the ideas of feed, metabolic rate and stochastic restart to the walker were added, features that have been gaining ground recently in the study of random processes. This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. The representation of stationary state was also performed in graphical form, thus obtaining the distribution function of probability required. In order to briefly approach the walker in a deadly process, a graph was produced that presents the function between the number of steps taken by a walker before his death and his metabolic capacity.Este artigo elucidou informações a respeito do movimento browniano no anel, algo ainda pouco explorado na literatura. Além disso, foram adicionadas as ideias de alimentação, taxa metabólica e reinício estocástico ao caminhante, características que vem ganhando espaço recentemente no estudo de processos aleatórios. Esse artigo realizou a estruturação das equações diferenciais parciais que regem tal processo para o caso de um caminhante imortal, além de posteriormente encontrar soluções analíticas para estas expressões. A representação do estado estacionário do caminhante também foi realizada na forma gráfica, obtendo assim as funções distribuição de probabilidade requeridas. Com o intuito de abordar brevemente o caminhante em um processo mortal, foi produzido um gráfico que apresenta a função entre o número de passos dados por um caminhante antes de sua morte e sua capacidade metabólica.

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 Limit theorems for solutions of stochastic differential equation problems

1980 ◽  
Vol 3 (1) ◽  
pp. 113-149 ◽  
Author(s):  
J. Vom Scheidt ◽  
W. Purkert
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Initial Value Problems ◽  
Limit Theorems ◽  
Eigenvalue Problems ◽  
Random Processes ◽  
Inhomogeneous Term ◽  
Initial Value ◽  
Linear Differential

In this paper linear differential equations with random processes as coefficients and as inhomogeneous term are regarded. Limit theorems are proved for the solutions of these equations if the random processes are weakly correlated processes.Limit theorems are proved for the eigenvalues and the eigenfunctions of eigenvalue problems and for the solutions of boundary value problems and initial value problems.

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