Parametric estimation for linear stochastic differential equations driven by sub-fractional Brownian motion

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Asymptotic Properties ◽  
Type Theorem ◽  
Parametric Estimation ◽  
Likelihood Estimator ◽  
Von Mises ◽  
Drift Parameter

AbstractWe investigate the asymptotic properties of the maximum likelihood estimator and Bayes estimator of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by a sub-fractional Brownian motion. We also obtain a Bernstein–von Mises type theorem for this class of processes.

Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion

2003 ◽  
Vol 11 (3) ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Asymptotic Properties ◽  
Type Theorem ◽  
Parametric Estimation ◽  
Likelihood Estimator ◽  
Von Mises ◽  
Drift Parameter

We investigate the asymptotic properties of the maximum likelihood estimator and Bayes estimator of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

scholarly journals Parameter Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Na Song ◽  
Zaiming Liu
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Asymptotic Properties ◽  
Regularity Conditions ◽  
Minimum Distance Estimator ◽  
Mixed Fractional Brownian Motion ◽  
Distance Estimator ◽  
Drift Parameter

We study the asymptotic properties of minimum distance estimator of drift parameter for a class of nonlinear scalar stochastic differential equations driven by mixed fractional Brownian motion. The consistency and limit distribution of this estimator are established as the diffusion coefficient tends to zero under some regularity conditions.

scholarly journals Fuzzy stochastic differential equations driven by fractional Brownian motion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Marek T. Malinowski ◽  
M. J. Ebadi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Stochastic Integral ◽  
Long Range Dependence ◽  
World Systems

AbstractIn this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

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