scholarly journals Hypercomplex systems and non-Gaussian stochastic solutions of χ-Wick-type (3+1)-dimensional modified Benjamin-Bona-Mahony equation

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 209-223
Author(s):  
Mohammed Zakarya
Keyword(s):  
White Noise ◽  
Wick Product ◽  
Hermite Transform ◽  
Wave Solutions ◽  
Hypercomplex System ◽  
Non Gaussian ◽  
Type 3

In this paper, we seek non-Gaussian stochastic solutions of ?-Wick-type stochastic (3+1)-dimensional modified Benjamin-Bona-Mahony equations. Using the generalized modified tanh-coth method, the connection between hypercomplex system and transforming white noise theory, ?-Wick product and ?-Hermite transform, we generate a new set of exact travelling non-Gaussian wave solutions for the (3+1)-dimensional modified Benjamin-Bona-Mahony equations. This set contains solutions with non-Gaussian parameters of exponential, hyperbolic, and trigonometric types.

scholarly journals Hypercomplex systems and non-Gaussian stochastic solutions of χ-Wick-type (3+1)-dimensional modified Benjamin-Bona-Mahony equation

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 209-223
Author(s):  
Mohammed Zakarya
Keyword(s):  
White Noise ◽  
Wick Product ◽  
Hermite Transform ◽  
Wave Solutions ◽  
Hypercomplex System ◽  
Non Gaussian ◽  
Type 3

In this paper, we seek non-Gaussian stochastic solutions of ?-Wick-type stochastic (3+1)-dimensional modified Benjamin-Bona-Mahony equations. Using the generalized modified tanh-coth method, the connection between hypercomplex system and transforming white noise theory, ?-Wick product and ?-Hermite transform, we generate a new set of exact travelling non-Gaussian wave solutions for the (3+1)-dimensional modified Benjamin-Bona-Mahony equations. This set contains solutions with non-Gaussian parameters of exponential, hyperbolic, and trigonometric types.

scholarly journals Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 134 ◽  
Author(s):  
Praveen Agarwal ◽  
Abd-Allah Hyder ◽  
M. Zakarya ◽  
Ghada AlNemer ◽  
Clemente Cesarano ◽  
...  
Keyword(s):  
Exact Solutions ◽  
White Noise ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Hermite Transform ◽  
Wave Solutions ◽  
White Noise Functional

In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions.

scholarly journals White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended G ′ / G -Expansion Method

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Zhao Li ◽  
Peng Li ◽  
Tianyong Han
Keyword(s):  
White Noise ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Hermite Transform ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
White Noise Functional

In this paper, white noise functional solutions of Wick-type stochastic fractional mixed KdV-mKdV equations have been obtained by using the extended G ′ / G -expansion method and the Hermite transform. Firstly, the Hermite transform is used to transform Wick-type stochastic fractional mixed KdV-mKdV equations into deterministic fractional mixed KdV-mKdV equations. Secondly, the exact traveling wave solutions of deterministic fractional mixed KdV-mKdV equations are constructed by applying the extended G ′ / G -expansion method. Finally, a series of white noise functional solutions are obtained by the inverse Hermite transform.

scholarly journals EMD OF GAUSSIAN WHITE NOISE: EFFECTS OF SIGNAL LENGTH AND SIFTING NUMBER ON THE STATISTICAL PROPERTIES OF INTRINSIC MODE FUNCTIONS

2009 ◽  
Vol 01 (04) ◽  
pp. 517-527 ◽  
Author(s):  
GASTÓN SCHLOTTHAUER ◽  
MARÍA EUGENIA TORRES ◽  
HUGO L. RUFINER ◽  
PATRICK FLANDRIN
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Kernel Smoothing ◽  
Gaussian White Noise ◽  
Large Data ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Non Gaussian ◽  
Data Length ◽  
Number Of Iterations

This work presents a discussion on the probability density function of Intrinsic Mode Functions (IMFs) provided by the Empirical Mode Decomposition of Gaussian white noise, based on experimental simulations. The influence on the probability density functions of the data length and of the maximum allowed number of iterations is analyzed by means of kernel smoothing density estimations. The obtained results are confirmed by statistical normality tests indicating that the IMFs have non-Gaussian distributions. Our study also indicates that large data length and high number of iterations produce multimodal distributions in all modes.

Statistical properties of the kinematics and dynamics of a random gravity-wave field

1975 ◽  
Vol 70 (2) ◽  
pp. 251-255 ◽  
Author(s):  
C. C. Tung
Keyword(s):  
Probability Density Function ◽  
Wave Field ◽  
Gravity Wave ◽  
Vertical Velocity ◽  
Dynamic Pressure ◽  
Kinematics And Dynamics ◽  
Vertical Acceleration ◽  
Vertical Velocity Component ◽  
Wave Solutions ◽  
Non Gaussian

The probability density function and the first three statistical moments of the velocity, acceleration and dynamic pressure are obtained for a Gaussian, stationary, homogeneous, random gravity-wave field in deep water, using infinitesimal wave solutions. It is shown that the velocity, acceleration and pressure are non-Gaussian. While the horizontal accelerations and vertical velocity component are of zero mean and unskewed, the dynamic pressure, vertical acceleration and horizontal velocity components are skewed and have non-zero mean.

scholarly journals Filtering with a limiter

1998 ◽  
Vol 11 (3) ◽  
pp. 289-300 ◽  
Author(s):  
R. Liptser ◽  
P. Muzhikanov
Keyword(s):  
Weak Convergence ◽  
Diffusion Process ◽  
White Noise ◽  
Discrete Time ◽  
Diffusion Approximation ◽  
Conditional Expectation ◽  
Gaussian White Noise ◽  
Sampling Step ◽  
Non Gaussian ◽  
Filtering Problem

We consider a filtering problem for a Gaussian diffusion process observed via discrete-time samples corrupted by a non-Gaussian white noise. Combining the Goggin's result [2] on weak convergence for conditional expectation with diffusion approximation when a sampling step goes to zero we construct an asymptotic optimal filter. Our filter uses centered observations passed through a limiter. Being asymptotically equivalent to a similar filter without centering, it yields a better filtering accuracy in a prelimit case.

AN EXTENDED STOCHASTIC INTEGRAL AND A WICK CALCULUS ON PARAMETRIZED KONDRATIEV-TYPE SPACES OF MEIXNER WHITE NOISE

2008 ◽  
Vol 11 (04) ◽  
pp. 541-564 ◽  
Author(s):  
N. A. KACHANOVSKY
Keyword(s):  
White Noise ◽  
Stochastic Equation ◽  
Stochastic Integral ◽  
Holomorphic Functions ◽  
Generalized Functions ◽  
Wick Product ◽  
Stochastic Integration ◽  
Type Spaces ◽  
Wick Calculus

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".

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