Limiting measure and stationarity of solutions to stochastic evolution\n equations with Volterra noise

2017/06/18 by Petr Čoupek, Čoupek, Petr
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H05 #60H15 #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1706.05716

openalex publication_date 2017/06/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Large-time behaviour of solutions to stochastic evolution equations driven by\ntwo-sided regular Volterra processes is studied. The solution is understood in\nthe mild sense and takes values in a separable Hilbert space. Sufficient\nconditions for the existence of limiting measure and strict stationarity of the\nsolution process are found and an example for which these conditions are also\nnecessary is provided. The results are further applied to the heat equation\ndriven by the two-sided Rosenblatt process.\n

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

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