Recursive parameter estimation in the trend coefficient of a diffusion process

2010 ◽  
Vol 17 (4) ◽  
pp. 683-704
Author(s):  
Nanuli Lazrieva ◽  
Teimuraz Toronjadze
Keyword(s):  
Parameter Estimation ◽  
Diffusion Process ◽  
Asymptotic Properties ◽  
Recursive Estimation ◽  
Dimensional Parameter ◽  
One Dimensional ◽  
Recursive Parameter Estimation ◽  
Special Cases ◽  
Trend Coefficient ◽  
Recursive Estimators

Abstract The recursive estimation problem of a one-dimensional parameter in the trend coefficient of a diffusion process is considered. The asymptotic properties of recursive estimators are derived, based on the results on the asymptotic behaviour of a Robbins–Monro type SDE. Various special cases are considered.

scholarly journals Rate of Convergence in Recursive Parameter Estimation Procedures

2007 ◽  
Vol 14 (4) ◽  
pp. 721-736
Author(s):  
Teo Sharia
Keyword(s):  
Parameter Estimation ◽  
Stochastic Processes ◽  
Rate Of Convergence ◽  
Discrete Time ◽  
Recursive Estimation ◽  
Estimation Of Parameters ◽  
Recursive Parameter Estimation ◽  
Estimation Procedures

Abstract This paper is concerned with the rate of convergence of recursive estimation procedures for parameters of discrete time stochastic processes. Applications to estimation of parameters in several models are presented to illustrate the theory.

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

On the threshold strategies in optimal stopping problems for diffusion processes

2017 ◽  
Vol 54 (3) ◽  
pp. 963-969 ◽  
Author(s):  
Vadim Arkin ◽  
Alexander Slastnikov
Keyword(s):  
Diffusion Process ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Payoff Function ◽  
Threshold Strategy ◽  
One Dimensional ◽  
Stopping Set ◽  
Optimal Stopping Problems ◽  
Necessary And Sufficient

Abstract We study a problem when the optimal stopping for a one-dimensional diffusion process is generated by a threshold strategy. Namely, we give necessary and sufficient conditions (on the diffusion process and the payoff function) under which a stopping set has a threshold structure.

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