Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Abstract

Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.

Stabilization of diffusion stochastic dynamic information systems with account of external random disturbances

“…where 𝔽(𝑡, 𝑥, 𝑦, 𝑢) is an integral function defined in domain (8), 𝑢 ∈ ℝ 2 , is 𝔼{⋅/⋅} a conditional mathematical expectation [2] ; 𝑢[𝑡] = 𝑢�𝑡, 𝑥(𝑡), 𝑦(𝑡), 𝑓 𝑖 (𝜉 𝑖 )�is random control implemented by system (1) for 𝑢 = 𝑢(𝑡, 𝑥, 𝑦), 𝑓 𝑖 �𝜉 𝑖 (𝜔)�are given random variables with law (6).…”

Hyperbolastic Models from a Stochastic Differential Equation Point of View

“…Thus, from the logistic and Weibull equations, Barrera et al [28,29] introduced the hyperbolastic diffusion processes of type I and III. Likewise, and following this same idea, a multisigmoidal stochastic version of the logistic process has been obtained (Di Crescenzo et al [30]) as well as a diffusion processes linked to the oscillabolastic curve (Barrera et al [31]).…”