1,720,965 research outputs found
Positivity preserving stochastic θ-methods for selected SDEs
No full textSeveral applications are modelled by stochastic differential equations with positive solutions. Numerical methods, able to preserve positivity, are absolutely needed in this case, in order to retain the intrinsic meaning of the solution in the spirit of the underlying application. This paper discusses the ability of stochastic θ-Milstein methods to generate positive sequences of numerical approximations, when they are applied to models with affine drift and square root diffusion. Moreover, we provide a class of θ-methods able to preserve the positivity of a jump extended nonlinear CIR model. Numerical experiments confirm the theoretical analysis
A Numerical Scheme for Harmonic Stochastic Oscillators Based on Asymptotic Expansions
No full textIn this work, we provide a numerical method for discretizing linear stochastic oscillators with high constant frequencies driven by a nonlinear time-varying force and a random force. The presented method is constructed by starting from the variation of constants formula, in which highly oscillating integrals appear. To provide a suited discretisation of this type of integrals, we propose quadrature rules based on asymptotic expansions. Theoretical considerations and numerical experiments comparing the method with a standard approach on physical models are introduced
On the numerical structure preservation of nonlinear damped stochastic oscillators
Full text linkThe paper is focused on analyzing the conservation issues of stochastic-methods when applied to nonlinear damped stochastic oscillators. In particular, we are interested in reproducing the long-term properties of the continuous problem over its discretization through stochastic-methods, by preserving the correlation matrix. This evidence is equivalent to accurately maintaining the stationary density of the position and the velocity of a particle driven by a nonlinear deterministic forcing term and an additive noise as a stochastic forcing term. The provided analysis relies on a linearization of the nonlinear problem, whose effectiveness is proved theoretically and numerically confirmed
Filon quadrature for stochastic oscillators driven by time-varying forces
No full textIn this work, we propose a trigonometric stochastic numerical method for linear oscillators with high constant frequencies, driven by a nonlinear time-varying force and a random force. The scheme is obtained by applying the variation-of-constants formula and Filon quadrature, that is notoriously more effective for oscillating integrands. The development of the scheme and its analysis is equipped by numerical experiments on popular related physical models, confirming the effectiveness of the approach
Two-step Runge-Kutta methods for stochastic differential equations
No full textWe introduce a theory of two-step Runge-Kutta (TSRK) methods for stochastic differential equations, arising from the perturbation of the corresponding TSRK methods for deterministic problems. We present a proof of convergence and study the mean-square stability properties. Numerical experiments confirming the theoretical results are provided
Computing the closest real normal matrix and normal completion
No full textIn this article, we consider the problems (unsolved in the literature) of computing the nearest normal matrix X to a given non-normal matrix A, under certain constraints, that are (i) if A is real, we impose that also X is real; (ii) if A has known entries on a given sparsity pattern Ω and unknown/uncertain entries otherwise, we impose to X the constraint xij = aij for all entries (i,j) in the pattern Ω. As far as we know, there do not exist in the literature specific algorithms aiming to solve these problems. For the case in which all entries of A can be modified, there exists an algorithm by Ruhe, which is able to compute the closest normal matrix. However, if A is real, the closest computed matrix by Ruhe’s algorithm might be complex, which motivates the development of a different algorithm preserving reality. Normality is characterized in a very large number of ways; in this article, we consider the property that the square of the Frobenius norm of a normal matrix is equal to the sum of the squares of the moduli of its eigenvalues. This characterization allows us to formulate as equivalent problem the minimization of a functional of an unknown matrix, which should be normal, fulfill the required constraints, and have minimal distance from the given matrix A
A long term analysis of stochastic theta methods for mean reverting linear process with jumps
No full textIn this paper a relative analysis of moments reversion of the class of theta methods is provided for an stochastic differential equation with Poisson-driven jumps. We first determine under which conditions the first and second moments revert to steady state values. Second, we consider two different classes of implicit theta methods; theta-Euler method, and compensated theta-Euler method, and derive closed-form expressions for the conditional and asymptotic means and variances of considered methods. We provide a full analysis about the possibility to find methods able to replicate such long-terms quantities. Finally, to verify our theoretical results numerical experiments are given
DESTABILISING NONNORMAL STOCHASTIC DIFFERENTIAL EQUATIONS
Full text linkIn this article we address the stability of linear stochastic differential equations. In particular, we focus our attention on non-normality in stochastic differential equations. Following Higham and Mao we study a test problem for non-normal stochastic differential equations, that is stable without noise, and prove a property conjectured by Higham and Mao, that is that an exponentially small (in the dimension) noise term is able to destabilise in a mean-square sense the solution of the SDE
Recensione a A. Scalone, C. De Angelis, D. Porena, G. Stella (a cura di A. Carrino), Legalità e legittimità nell’interpretazione costituzionale, Milano, Mimesis, 2019, pp. 166
No full textRecensione a A. Scalone, C. De Angelis, D. Porena, G. Stella (a cura di A. Carrino), Legalità e legittimità nell’interpretazione costituzionale, Milano, Mimesis, 2019, pp. 16
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