scholarly journals Simultaneous determination of the drift and diffusion coefficients in stochastic differential equations

2017 ◽  
Vol 33 (9) ◽  
pp. 095006 ◽  
Author(s):  
Michel Cristofol ◽  
Lionel Roques
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Simultaneous Determination ◽  
Diffusion Coefficients ◽  
And Diffusion

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process

2020 ◽  
Vol 26 (1) ◽  
pp. 33-47
Author(s):  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
Maximum Process ◽  
And Diffusion

AbstractThe aim of this paper is to show the approximation of Euler–Maruyama {X_{t}^{n}} for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero

2018 ◽  
Vol 24 (4) ◽  
pp. 249-262
Author(s):  
Mohsine Benabdallah ◽  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Local Time ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
And Diffusion

Abstract We present the Euler–Maruyama approximation for one-dimensional stochastic differential equations involving the local time at point zero. Also, we prove the strong convergence of the Euler–Maruyama approximation whose both drift and diffusion coefficients are Lipschitz. After that, we generalize to the non-Lipschitz case.

scholarly journals On Stochastic Differential Equations Generating Non-gaussian Continuous Markov Process

2021 ◽  
Vol 17 ◽  
pp. 65-68
Author(s):  
Vladimir Lyandres
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
Function Estimation ◽  
Stationary Probability Distribution ◽  
Nonlinear Stochastic Differential Equations ◽  
Continuous Markov Process ◽  
Non Gaussian ◽  
The Given ◽  
And Diffusion

Continuous Markov processes widely used as a tool for modeling random phenomena in numerous applications, can be defined as solutions of generally nonlinear stochastic differential equations (SDEs) with certain drift and diffusion coefficients which together governs the process’ probability density and correlation functions. Usually it is assumed that the diffusion coefficient does not depend on the process' current value. For presentation of non-Gaussian real processes this assumption becomes undesirable, leads generally to complexity of the correlation function estimation. We consider its analysis for the process with particular pairs of the drift and diffusion coefficients providing the given stationary probability distribution of the considered process

Determination of mobility and diffusion coefficients of Ar+ and Ar2+ ions in argon gas

2020 ◽  
Vol 23 (2) ◽  
pp. 143-151
Author(s):  
Jamiyanaa Dashdorj ◽  
William C. Pfalzgraff ◽  
Aaron Trout ◽  
Delenn Fingerlow ◽  
Michelle Cordier ◽  
...  
Keyword(s):  
Diffusion Coefficients ◽  
Argon Gas ◽  
And Diffusion

Ein neues Verfahren zur Berechnung der Diffusionskoeffizienten in Multikomponentensystemen aus Meßdaten der quasistationären Diffusion / A new procedure for the determination of diffusion coefficients from quasi-stationary diffusion measurements in multicomponent systems

1975 ◽  
Vol 30 (4) ◽  
pp. 561-566
Author(s):  
W. Meiske ◽  
W. Schmidt ◽  
E. Kahrig
Keyword(s):  
Differential Equations ◽  
Diffusion Coefficients ◽  
Multicomponent Systems ◽  
Equivalent System ◽  
System Of Integral Equations ◽  
Component System ◽  
Flow Equations ◽  
Stationary Diffusion ◽  
Numerical Performance

Abstract Diffusion in an (n+1) -component system is described by Onsager's flow equations the integration of which leads in the case of quasi-stationarity to the differential equations d(Δc)/dt=-βD̅Δ c (Δc: vector of concentration differences between the compartments of the cell, D̅: matrix of integral diffusion coefficients, β: apparatus constant). Several procedures are known to determine these diffusion coefficients from such equations but all of them have certain disadvantages. In this paper a new method is described to compute the integral diffusion coefficients, which starts from the associated equivalent system of integral equations. The mathematical formalism is simple, and its numerical performance does not become more difficult with an increasing number of components of the system.

scholarly journals Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Marek T. Malinowski
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Lipschitz Condition ◽  
New Type ◽  
And Diffusion

We introduce and analyze a new type of fuzzy stochastic differential equations. We consider equations with drift and diffusion terms occurring at both sides of equations. Therefore we call them the bipartite fuzzy stochastic differential equations. Under the Lipschitz and boundedness conditions imposed on drifts and diffusions coefficients we prove existence of a unique solution. Then, insensitivity of the solution under small changes of data of equation is examined. Finally, we mention that all results can be repeated for solutions to bipartite set-valued stochastic differential equations.

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