Results 221 to 230 of about 4,492 (252)

On the approximation of invariant measures

Journal of Statistical Physics, 1992
Given a discrete dynamical system defined by the map \(\tau : X \rightarrow X\), the density of the absolutely continuous (a.c.) invariant measure (if it exists) is the fixed point of the Frobenius-Perron operator defined on \(L^1(X)\). Ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a ...
Hunt, Fern Y., Miller, Walter M.
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Approximation and invariant measures

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1965
We prove certain approximation theorems for the class of invertible, measurable, and non-singular transformations of the unit interval. The main results concern the approximation of such transformations by those having no a-finite invariant measure absolutely continuous with respect to Lebesgue measure. We are indebted to A.
Chacon, R. V., Friedman, N.
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Numerical approximation of invariant measures for hybrid diffusion systems

IEEE Transactions on Automatic Control, 2005
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Gang George Yin, Xuerong Mao, K. Karen Yin   +2 more
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Numerical Approximation to Invariant Measures

2009
Continuing with the development in Chapter 5, this chapter is devoted to additional properties of numerical approximation algorithms for switching diffusions, where continuous dynamics are intertwined with discrete events. In this chapter, we establish that if the invariant measure exists, under suitable conditions, the sequence of iterates obtained ...
G. George Yin, Chao Zhu
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Algorithms for approximation of invariant measures for IFS

manuscripta mathematica, 2004
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Approximation Procedures for Invariant Probability Measures

2003
In this chapter we consider a MC on a LCS metric space X with t.p.f. P. Suppose for the time being that t E 11I (X) is an ergodic invariant p.m. for P (see Definition 2.4.1). We address the following issue. Given f E L1(µ), we want to evaluate f f d,u knowing only that the ergodic invariant p.m. p exists but h itself is not known.
Onésimo Herná-Lerma, Jean Bernard Lasserre   +1 more
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Truncation approximations of invariant measures for Markov chains

Journal of Applied Probability, 1998
Let P be the transition matrix of a positive recurrent Markov chain on the integers, with invariant distribution π. If (n)P denotes the n x n ‘northwest truncation’ of P, it is known that approximations to π(j)/π(0) can be constructed from (n)P, but these are known to converge to the probability distribution itself in special cases only.
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Fractal approximation by absolutely continuous invariant measures

Physics Letters A, 1990
Abstract Let {X:τ1, …, τN} be an iterated function system with attractor S. We associate probabilities p1, …, pN with τ1, …, τN, respectively. Let M ( X ) be the space of Borel probability measures on X, and let M: M ( X )→ M ( X ) be the Markov operator associated with the iterated function system and its probabilities given ...
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Approximation of invariant measures of stochastic evolution processes: Time discretization

Proceedings of the American Mathematical Society
This paper deals with approximation of invariant measures of stochastic evolution processes. Under certain conditions, we demonstrate that any limit point of invariant measures of the time discrete approximations, i.e., numerical scheme, must be an invariant measure of the underlying continuous stochastic evolution processes as the step size approaches
Li, Dingshi, Pu, Zhe, Mi, Shaoyue
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An adaptive subdivision technique for the approximation of attractors and invariant measures

Computing and Visualization in Science, 1998
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Dellnitz, Michael, Junge, Oliver
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