Gauss-Markov processes as space-time scaled stationary\n Ornstein-Uhlenbeck processes

2014/09/25 by Mátyás Barczy, Barczy, Matyas, Peter Kern +1
Economics, Econometrics and Finance · Mathematics · #60G10 #60G15 #60J65 #FOS: Mathematics #Financial Risk and Volatility Modeling #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1409.7253

openalex publication_date 2014/09/25 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

We present a class of Gauss-Markov processes which can be represented as\nspace-time scaled stationary Ornstein-Uhlenbeck processes defined on the real\nline. We give several explicit examples of the representation for certain Gauss\nbridge processes. As an application, we derive a formula for the density\nfunction of the supremum location of certain standardized Gauss-Markov\nprocesses on compact time intervals. We also present some sufficient conditions\nunder which mean centered Gauss-Markov processes take zero at a fixed time with\nprobability one.\n

Citations

• Conditioning of Gaussian processes and a zero area Brownian bridge

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