Stochastic Models and Random Evolution Equations

1992 ◽  
pp. 1-23
Author(s):  
N. Bellomo ◽  
Z. Brzezniak ◽  
L. M. de Socio
Keyword(s):  
Stochastic Models ◽  
Evolution Equations ◽  
Random Evolution

scholarly journals MULTIFRACTAL FLUCTUATIONS IN FINANCE

2000 ◽  
Vol 03 (03) ◽  
pp. 361-364 ◽  
Author(s):  
FRANCOIS SCHMITT ◽  
DANIEL SCHERTZER ◽  
SHAUN LOVEJOY
Keyword(s):  
Brownian Motion ◽  
Exchange Rate ◽  
Foreign Exchange ◽  
Stochastic Models ◽  
Evolution Equations ◽  
Foreign Exchange Rate ◽  
Scaling Exponent ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Multiplicative Processes

We consider the structure functions S(q)(τ), i.e. the moments of order q of the increments X(t + τ)-X(t) of the Foreign Exchange rate X(t) which give clear evidence of scaling (S(q)(τ)∝τζ(q)). We demonstrate that the nonlinearity of the observed scaling exponent ζ(q) is incompatible with monofractal additive stochastic models usually introduced in finance: Brownian motion, Lévy processes and their truncated versions. This nonlinearity correspond to multifractal intermittency yielded by multiplicative processes. The non-analyticity of ζ(q) corresponds to universal multifractals, which are furthermore able to produce "hyperbolic" pdf tails with an exponent qD > 2. We argue that it is necessary to introduce stochastic evolution equations which are compatible with this multifractal behaviour.

Random evolution equations in hydrology

1990 ◽  
Vol 39 (3) ◽  
pp. 97s-122s ◽  
Author(s):  
Sergio E. Serrano ◽  
T.E. Unny
Keyword(s):  
Evolution Equations ◽  
Random Evolution

scholarly journals Functional random evolution equations in Frechet spaces

2018 ◽  
pp. 128-137
Author(s):  
Said Abbas ◽  
Amaria Arara ◽  
Mouffak Benchohra ◽  
Fatima Mesri
Keyword(s):  
Evolution Equations ◽  
Random Evolution ◽  
Fréchet Spaces

scholarly journals Weak pullback mean random attractors for stochastic evolution equations and applications

2021 ◽  
pp. 2240001
Author(s):  
Anhui Gu
Keyword(s):  
Stochastic Models ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Random Attractors ◽  
Porous Media Equations ◽  
Stochastic Reaction

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of weak pullback mean random attractors for some stochastic models such as stochastic reaction–diffusion equations, the stochastic [Formula: see text]-Laplace equation and stochastic porous media equations are established.

Large deviations for random evolution equation in Besov-Orlicz space

2020 ◽  
pp. 357-387
Author(s):  
Dina Miora Rakotonirina ◽  
Jocelyn Hajaniaina Andriatahina ◽  
Rado Abraham Randrianomenjanahary ◽  
Toussaint Joseph Rabeherimanana
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Orlicz Space ◽  
Evolution Equations ◽  
Random Evolution ◽  
Young Function ◽  
Large Deviations Principle

In this paper, we develop a large deviations principle for random evolution equations to the Besov-Orlicz space $\mathcal{B}_{M_2, w}^{v, 0}$ corresponding to the Young function $M_2(x)=\exp(x^2)-1$.

Support Theorem for Random Evolution Equations in Hölderian Norm

2017 ◽  
Vol 20 (3) ◽  
pp. 1-15
Author(s):  
J Andriatahina ◽  
R Rakotoarisoa ◽  
T Rabeherimanana
Keyword(s):  
Evolution Equations ◽  
Random Evolution ◽  
Support Theorem
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