Sentence examples for fractional process from inspiring English sources

We consider the parameter estimation problem for a special fractional process, i.e., fractional Ornstein-Uhlenbeck process, which satisfies the following stochastic differential equation: d X t = θ X t d t + ε d B t H, 0 ≤ t ≤ T, X 0 = x 0, (1).

Consider the parameter estimation problem for a special fractional process, i.e., fractional Ornstein-Uhlenbeck type process X = { X t, 0 ≤ t ≤ T }, which satisfies the following stochastic integral equation: X t = x 0 + θ ∫ 0 t X s d s + ε B t H, 0 ≤ t ≤ T, (1).

The limit results relate to tempered fractional processes that include tempered fractional Brownian motion and tempered fractional diffusions.

Essentially, the problem of estimating the Hurst parameter in fractional processes has been extensively studied (see Shen et al. [44]; Kubilius and Mishura [45]; Salomónab and Fortc [46]).

More recently, there has been increased interest in studying asymptotic properties of LSE for the drift parameter in the univariate case with fractional processes (see, Azmoodeh and Morlanes [16]; Cheng et al. [17]).

In classical fractional operators, the fractionalizing process depends on iterating the weighted usual integrals or some local type derivatives in the way to get the factorial function and then replace it by the gamma function.

We demonstrate the performance of the proposed SMC on the stochastic volatility model driven by a fractional Gaussian process filtered by an ARMA p,q) process.

With the first formulation, the long-memory processes are described as stationary increments of self-similar models, of which the fractional Gaussian process (fGp) is a prime example.

The results of the study showed that due to the freezing and fractional melting process, hardness salts were concentrated by 1.30 times (the III fraction of the water sample taken from the Vardenis river mouth) to 2.40 times (the III fraction of the water sample taken from the Karchaghbyur river source) compared to the same parameter values in the water samples before the freezing melting process.

Tholeiitic magma underwent a fractional crystallization process that deposited layers of ultramafic rocks overlain by gabbroic and anorthositic layers.

A methodology is presented for the synthesis of fractional crystallisation process with heat integration.