Search results for "mathematical analysis"
showing 10 items of 2409 documents
Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach
2011
In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.
An Improved Method for Estimating the Time ACF of a Sum of Complex Plane Waves
2010
Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we pr…
Weak Maximum Principle and Application to Swimming at Low Reynolds Number
2018
We refer to [9, 42, 46] for more details about the general concepts and notations introduced in this section.
Semi-discrete Galerkin approximation method applied to initial boundary value problems for Maxwell's equations in anisotropic, inhomogeneous media
1981
SynopsisIn this paper the semi-discrete Galerkin approximation of initial boundary value problems for Maxwell's equations is analysed. For the electric field a hyperbolic system of equations is first derived. The standard Galerkin method is applied to this system and a priori error estimates are established for the approximation.
Non Linear Systems Under Complex α-Stable Le´vy White Noise
2003
The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME
Itô-Stratonovitch Formula for the Wave Equation on a Torus
2010
We give an Ito-Stratonovitch formula for the wave equation on a torus, where we have no stochastic process associated to this partial differential equation. This gives a generalization of the classical Ito-Stratonovitch equation for diffusion in semi-group theory established by ourself in [18], [20].
Random Walk and Diffusion
2014
The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.
Bounds for Bessel functions
1989
We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.
COMPLEX CONVEXITY AND VECTOR-VALUED LITTLEWOOD–PALEY INEQUALITIES
2003
Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.
Explicit expressions for Sturm-Liouville operator problems
1987
Throughout this paper H will denote a complex separable Hilbert space and L(H) denotes the algebra of all bounded linear operators on H. If T lies in L(H), its spectrum σ(T) is the set of all complex numbers z such zI–T is not invertible in L(H) and its compression spectrum σcomp(T) is the set of all complex numbers z such that the range (zI-T)(H) is not dense in H ([3, p. 240]). This paper is concerned with the Sturm–Liouville operator problemwhere λ is a complex parameter and X(t), Q, Ei, Fi for i = l,2, and t∈[0,a], are bounded operators in L(H). For the scalar case, the classical Sturm-Liouville theory yields a complete solution of the problem, see [4], and [7]. For the finite-dimension…