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Kolmogorov equation and large-time behaviour for fractional brownian motion driven linear sde’s

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Abstract

We consider a stochastic process X xt which solves an equation

$$dX_t^x = AX_t^x dt + \Phi dB_t^H \quad X_0^x = x$$

where A and Φ are real matrices and BH is a fractional Brownian motion with Hurst parameter H ∈ (1/2,1). The Kolmogorov backward equation for the function u(t,x) = \(H \in \left( {{1 \mathord{\left/ {\vphantom {1 {2,1}}} \right. \kern-\nulldelimiterspace} {2,1}}} \right)\)f(X xt ) is derived and exponential convergence of probability distributions of solutions to the limit measure is established.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8

    Michal Vyroai

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  1. Michal Vyroai
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Additional information

This research has been supported by the grant no. 201/01/1197 of the Grant Agency of the Czech Republic.

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Vyroai, M. Kolmogorov equation and large-time behaviour for fractional brownian motion driven linear sde’s. Appl Math 50, 63–81 (2005). https://doi.org/10.1007/s10492-005-0004-4

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  • DOI: https://doi.org/10.1007/s10492-005-0004-4

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