On large deviations of solutions of nonlinear stochastic equations

1990 ◽  
Vol 50 (2) ◽  
pp. 1476-1490
Author(s):  
V. M. Imaikin ◽  
A. I. Komech
Keyword(s):  
Large Deviations ◽  
Stochastic Equations ◽  
Nonlinear Stochastic Equations

Jacobian elliptic function expansion solutions of nonlinear stochastic equations

2005 ◽  
Vol 26 (2) ◽  
pp. 551-558 ◽  
Author(s):  
Cai-Min Wei ◽  
Zun-Quan Xia ◽  
Nai-Shuo Tian
Keyword(s):  
Elliptic Function ◽  
Stochastic Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion ◽  
Nonlinear Stochastic Equations

Ergodicity for Nonlinear Stochastic Equations in Variational Formulation

2005 ◽  
Vol 53 (2) ◽  
pp. 121-139 ◽  
Author(s):  
Viorel Barbu ◽  
Giuseppe Da Prato
Keyword(s):  
Variational Formulation ◽  
Stochastic Equations ◽  
Nonlinear Stochastic Equations

scholarly journals Projective Stochastic Equations and Nonlinear Long Memory

2014 ◽  
Vol 46 (4) ◽  
pp. 1084-1105
Author(s):  
Ieva Grublytė ◽  
Donatas Surgailis
Keyword(s):  
Long Memory ◽  
Volterra Series ◽  
Bernoulli Shift ◽  
Moving Average ◽  
Stochastic Equations ◽  
Partial Sums ◽  
Martingale Transform ◽  
New Class ◽  
Moving Average Processes ◽  
Nonlinear Stochastic Equations

A projective moving average {Xt, t ∈ ℤ} is a Bernoulli shift written as a backward martingale transform of the innovation sequence. We introduce a new class of nonlinear stochastic equations for projective moving averages, termed projective equations, involving a (nonlinear) kernel Q and a linear combination of projections of Xt on ‘intermediate’ lagged innovation subspaces with given coefficients αi and βi,j. The class of such equations includes usual moving average processes and the Volterra series of the LARCH model. Solvability of projective equations is obtained using a recursive equality for projections of the solution Xt. We show that, under certain conditions on Q, αi, and βi,j, this solution exhibits covariance and distributional long memory, with fractional Brownian motion as the limit of the corresponding partial sums process.

A note on nonlinear stochastic equations in Hilbert spaces

1993 ◽  
Vol 17 (5) ◽  
pp. 387-394 ◽  
Author(s):  
Dariusz Ga̧tarek
Keyword(s):  
Hilbert Spaces ◽  
Stochastic Equations ◽  
Nonlinear Stochastic Equations

Asymptotic Analysis of Nonlinear Stochastic Equations With Rapidly Oscillating and Decaying Components

2003 ◽  
Author(s):  
N. Sri Namachchivaya ◽  
H. J. Van Roessel
Keyword(s):  
Dynamical System ◽  
Markov Process ◽  
Martingale Problem ◽  
Nonlinear Dynamical System ◽  
Stochastic Equations ◽  
Limiting Behavior ◽  
Nonlinear Dynamical ◽  
Nonlinear Stochastic Equations ◽  
Lower Dimensional ◽  
Quadratic And Cubic Nonlinearities

We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.

On Large Deviations for Systems of Itô Stochastic Equations

1992 ◽  
Vol 36 (4) ◽  
pp. 772-782
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Large Deviations ◽  
Stochastic Equations

scholarly journals Максимум энтропии в масштабно-инвариантных процессах с 1/f-=SUP=-alpha-=/SUP=--спектром мощности: влияние анизотропии белого шума

2019 ◽  
Vol 45 (9) ◽  
pp. 19
Author(s):  
В.П. Коверда ◽  
В.Н. Скоков
Keyword(s):  
Phase Transitions ◽  
White Noise ◽  
Power Spectra ◽  
Random Processes ◽  
Stochastic Equations ◽  
Alpha Power ◽  
Entropy Maximum ◽  
The Stability ◽  
Nonlinear Stochastic Equations

Large value fluctuations are modeled by a system of nonlinear stochastic equations describing the interacting phase transitions. Under the action of anisotropic white noise, random processes are formed with the 1/f^alpha dependence of the power spectra on frequency at values of the exponent from 0.7 to 1.7. It is shown that fluctuations with 1/f^alpha power spectra in the studied range of changes correspond to the entropy maximum, which indicates the stability of processes with 1/f^alpha power spectra at different values of the exponent alpha.

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