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Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations
[article]
2015
arXiv
pre-print
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This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics ...
These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be ...
The main tools used in this analysis are properties of the SDE solution and the following variation of constants formula for a mild solution of an inhomogeneous, linear differential equation on a Banach ...
arXiv:1502.05034v2
fatcat:2wxfuoplfzhcvbcg52lmr6zaue
Numerical approximation of random periodic solutions of stochastic differential equations
2017
Zeitschrift für Angewandte Mathematik und Physik
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In this paper, we discuss the numerical approximation of random periodic solutions (r.p.s.) of stochastic differential equations (SDEs) with multiplicative noise. ...
We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √(Δ t) in the mean-square sense in Euler-Maruyama method and Δ t in the Milstein method ...
reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. ...
doi:10.1007/s00033-017-0868-7
fatcat:wlz4ac4v3bbphmykpjgcg4ciwy
Numerical solution of random differential models
2011
Mathematical and computer modelling
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This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. ...
Conditions for the mean square convergence of the proposed method are established. ...
a b s t r a c t This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. ...
doi:10.1016/j.mcm.2010.12.037
fatcat:zk2pfyyme5hatovm2kklswl2em
Numerical solution of systems of random differential equations with Gaussian statistics
1985
Journal of Mathematical Analysis and Applications
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A direct approach is used to compute a numerical solution for a system of (nonlinear) ordinary differential equations with Gaussian statistics. ...
It is shown that for a large class of problems the accuracy of the solution can be made as great as desired by taking the step size h sufficiently small. B 1985 Academic Prerq Inc. 222 ...
Barry and Boyce [7] have a numerical method for certain differential equations with random boundaries. ...
doi:10.1016/0022-247x(85)90108-8
fatcat:zcgzgmtqyranrdfg5anz2idjby
Mean square numerical solution of random differential equations: Facts and possibilities
2007
Computers and Mathematics with Applications
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This paper deals with the construction of numerical solutions of random initial value differential problems. ...
The random Euler method is presented and the conditions for the mean square convergence are established. ...
This motivates the main goal of this paper that is to introduce the random Euler method for constructing reliable numerical solutions of the problem (1.1) in the sense that approximations be mean square ...
doi:10.1016/j.camwa.2006.05.030
fatcat:ziixx5t5pnf5hdrcntjykr5pa4
Solving linear and quadratic random matrix differential equations: A mean square approach
2016
Applied Mathematical Modelling
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Solving linear and quadratic random matrix differential equations: A mean square approach. Applied Mathematical Modelling. 40(21-22):9362-9377. ...
Abstract In this paper linear and Riccati random matrix differential equations are solved taking advantage of the so called L p -random calculus. ...
class of randomness, has been developed in recent years taking advantage of the mean square random calculus. ...
doi:10.1016/j.apm.2016.06.017
fatcat:65ylhcxhxba7rkqm7mefon3lxi
Symbolic and numeric scheme for solution of linear integro-differential equations with random parameter uncertainties and Gaussian stochastic process input
2018
Applied Mathematical Modelling
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The paper describes a theoretical apparatus and an algorithmic part of application of the Green matrix-valued functions for time-domain analysis of systems of linear stochastic integro-differential equations ...
The first one explicitly defines closed relations for symbolic and numeric computations of the conditional mean and covariance functions, and the second one calculates unconditional characteristics by ...
As it was said before, the main aim of numerical experiments performed by MCM is a numerical verification of the presented mathematical approach. ...
doi:10.1016/j.apm.2017.11.024
fatcat:qj32iyg2zzb65p2adx274uoqcm
Numerical Solution of Stiff ODEs with Physics-Informed RPNNs
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2108.01584v1 fatcat:zhk5dshotfbuxcqo2gruhuj7qy
We propose a numerical method based on physics-informed Random Projection Neural Networks for the solution of Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) with a focus on stiff ...
The numerical solution of the IVPs is obtained by constructing a system of nonlinear algebraic equations, which is solved with respect to the output weights by the Gauss-Newton method, using a simple adaptive ...
The estimation of the optimal output weights is achieved by solving a system of linear equations arising from a mean-squares minimization problem. ...
arXiv:2108.01584v2
fatcat:rtzek2qcara4df4mpq3xwmhojy
Extending the deterministic Riemann–Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations
2017
Chaos, Solitons & Fractals
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Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations. ...
The approach is based on a mean square chain rule, recently established, together with the random Fröbenius method. ...
the mean square derivative of a random power series in order to formally construct the solution 159 of the random fractional linear differential equation with a random initial condition. ...
doi:10.1016/j.chaos.2017.02.008
fatcat:2iuhoodokvap7nybx2swdoarhu
A Competitive Mean-Squared Error Approach to Beamforming
2007
IEEE Transactions on Signal Processing
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However this does not guarantee a small mean-squared error (MSE), hence on average their resulting signal estimateŝ(t) can be far from s(t). ...
However, this approach does not guarantee a small MSE, so that on average, the resulting estimate of s(t) may be far from s(t). ...
La Rosa for conducting the numerical examples in this paper. ...
doi:10.1109/tsp.2007.897883
fatcat:ggokauh6dfep3l22wxpnvvst4a
Analytic-Numerical Solution of Random Parabolic Models: A Mean Square Fourier Transform Approach
2018
Mathematical Modelling and Analysis
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This paper deals with the construction of mean square analytic-numerical solution of parabolic partial differential problems where both initial condition and coefficients are stochastic processes. ...
By using a random Fourier transform, an inf- nite integral form of the solution stochastic process is firstly obtained. ...
To achieve this goal, we use a mean square Fourier transform approach. ...
doi:10.3846/mma.2018.006
fatcat:lfmggz2u3zbwzbvhkqlnsplwdi
Mean-Squared Error Beamforming for Signal Estimation: A Competitive Approach
[chapter]
2005
Robust Adaptive Beamforming
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1.30) is also the solution in the case in which we have both an upper and lower bound on the norm xviii MEAN-SQUARED ERROR BEAMFORMING FOR SIGNAL ESTIMATION of s. ...
− mŝ) * R −1 (y − mŝ) +ŝ 2 E (a − m) * R −1 (a − m) = (y − mŝ) * R −1 (y − mŝ) +ŝ 2 Tr R −1 C . (1.84) Differentiating (1.84) with respect toŝ and equating to 0, we have that s = 1 Tr (R −1 C) + m * R ...
doi:10.1002/0471733482.ch5
fatcat:h7q5t3frmrcgtear7i3vkpd4pm
Solving the random diffusion model in an infinite medium: A mean square approach
2014
Applied Mathematical Modelling
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This paper deals with the construction of an analytic-numerical mean square solution of the random diffusion model in an infinite medium. ...
Mean square operational rules to the Fourier transform of a stochastic process are developed and stated. The main statistical moments of the stochastic process solution are also computed. ...
The theory and applications of random differential equations is a very active area of mathematical research and there are several different approaches, from the so-called stochastic differential approach ...
doi:10.1016/j.apm.2014.04.063
fatcat:dr3j5njuavacha2czj2nagpamy
Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach
2007
Polymer
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This paper describes a kinetic method to predict the z-average molecular mean square radius of gyration of tree-like polymers formed by irreversible reactions, assuming Gaussian chains. ...
An automated method for the solution of those equations is valid both before as well as after gelation for complex kinetic schemes. ...
A general procedure for solving the resulting partial differential equations by the method of characteristics is a key point in this approach. ...
doi:10.1016/j.polymer.2007.01.033
fatcat:7o5454satfc2dkcimvu7c72nim
Numerical Solution of Stochastic Differential Equations
[chapter]
2013
Introduction to Stochastic Analysis
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This chapter is an introduction and survey of numerical solution methods for stochastic differential equations. ...
We include a review of fundamental concepts, a description of elementary numerical methods and the concepts of convergence and order for stochastic differential equation solvers. ...
Summary Numerical methods for the solution of stochastic differential equations are essential for the analysis of random phenomena. ...
doi:10.1002/9781118603338.ch13
fatcat:ku7bvcu65vcntkluw3cej4qmwq
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