Differential and Integral Equations

Invariant measures for stochastic functional differential equations with superlinear drift term

Abdelhadi Es-Sarhir, Michael Scheutzow, and Onno van Gaans

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Abstract

We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove tightness and Feller property of the segment process to show existence of an invariant measure.

Article information

Source
Differential Integral Equations, Volume 23, Number 1/2 (2010), 189-200.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019393

Mathematical Reviews number (MathSciNet)
MR2588808

Zentralblatt MATH identifier
1240.34396

Subjects
Primary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60] 60H20: Stochastic integral equations 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}

Citation

Es-Sarhir, Abdelhadi; van Gaans, Onno; Scheutzow, Michael. Invariant measures for stochastic functional differential equations with superlinear drift term. Differential Integral Equations 23 (2010), no. 1/2, 189--200. https://projecteuclid.org/euclid.die/1356019393


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