By Gerencser L., Matyas Z.
Inventory exchanges are modeled as nonlinear closed-loop platforms wherethe plant dynamics is outlined through recognized inventory industry rules and the activities ofagents are in keeping with their ideals and behaviour. the choice of the brokers may perhaps containa random point, hence we get a nonlinear stochastic suggestions process. The marketis in equilibrium while the activities of the brokers make stronger their ideals at the pricedynamics. Assuming that linear predictors are used for prediction of the fee process,a stochastic approximation process for locating industry equilibrium is described.The proposed process is analyzed utilizing the idea of Benveniste et al. (Adaptivealgorithms and stochastic approximations. Springer, Berlin, 1990).Asimulation resultis additionally provided.
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Additional resources for A behavioral stock market model
Remarks. 1. The semi-concave stability holds for vanishing viscosity regularizations, and hence the exact viscosity solutions, in each direction. Analogous results hold for OSLC stability for convex conservation laws. 2. e. Dx2 ϕ0 ≤ m. 2 with dβ Ci (T ) = (m−1 + αT ) α , i = 0, 1. Equipped with these bounds, we revisit our error estimates in Sect. 1. 15). 2, and the explicit value of Ci ’s above, we arrive at the explicit L1 -error bound: ϕ (·, t) − ϕ(·, t) T dβ L1 ≤ 2 · |Ω| · (m−1 + αT ) α 0 ≤ t ≤ T.
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We note that, the last inequality with α = β yields ϕ (·, t) − ϕ(·, t) L1 = O( td ln t). -T. Lin, E. 3. The above arguments fail in case the upper semi-concave bound of the 1 initial data m = ∞, for k(t) = αt ∈ / L1 [0, T ]. ) This enables to extend our results to include such initial sharp corners (m = ∞) along the lines of . 1) satisfy the following discrete version of semi-concave stability. 1, is essential for studying the semi-concave stability of ﬁnite difference approximations. 1). 4) Wh,ξ (t) ≤ Wh,ξ (0), 2 Wh,ξ (t) := sup Dξ,h ϕ (x, t) .