Affine processes also include all Lévy processes. Informally, a process X on a state space D is affine if its characteristic function can be written as E[eiu Xt ] = eφ(t,u)+ψ(t,u) X0 for some complex-valued
Therefore, any model that correctly describes the contact stiffness on the largest scale and reproduces the gradient of the surface profile on the smallest scale, is eligible for the study of frictional processes (examples of models based on the two-scale nature of frictional contacts can be ...
Typically, the functions φ and ψ are solutions of an associated pair of generalised Riccati equations that can be solved numerically. Affine processes on the state-space H+, as considered in this work, have been first introduced and studied in Cox et al. [17]. Their construc- tion is ...
γ1 and γ2 introduce an exponential memory characteristic to signify the weighted importance of the preceding training observation data, leading to smooth model adaptation behavior. Their values can be set properly in the range of one and zero (i.e., 0<γ1⩽1, 0<γ2⩽1). γ1 = γ...
Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrase “in one embodiment” in various...
(x; (11 _> > 0), (2) as a simple linearized model of the projection of a rotationally symmetric Gaus- sian blob (where 11 and 12 are characteristic lengths in the x- and y-coordinate di- rections and g is the one-dimensional Gaussian, g(x; t) = (27rt)-U2 exp(-x2/2t))....