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

2003 ◽  
Vol 11 (3) ◽  
pp. 229-242 ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Parametric Estimation

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 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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