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Ergodicity of stochastic differential equations driven by fractional Brownian motion
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UNSPECIFIED (2005) Ergodicity of stochastic differential equations driven by fractional Brownian motion. ANNALS OF PROBABILITY, 33 (2). pp. 703-758. doi:10.1214/009117904000000892 ISSN 0091-1798.
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Official URL: http://dx.doi.org/10.1214/009117904000000892
Abstract
We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H is an element of (0, 1). A general framework is constructed to make precise the notions of "invariant measure" and "stationary state" for such a system. We then prove under rather weak dissipativity conditions that such an SIDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution toward the stationary one is (at least) algebraic. A lower bound on the exponent is also given.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ANNALS OF PROBABILITY | ||||
Publisher: | INST MATHEMATICAL STATISTICS | ||||
ISSN: | 0091-1798 | ||||
Official Date: | March 2005 | ||||
Dates: |
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Volume: | 33 | ||||
Number: | 2 | ||||
Number of Pages: | 56 | ||||
Page Range: | pp. 703-758 | ||||
DOI: | 10.1214/009117904000000892 | ||||
Publication Status: | Published |
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