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Thread: Stochatic Processes Ornstein-Uhlenbeck

  1. #1 Stochatic Processes Ornstein-Uhlenbeck 
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    Hello,
    I have an emergency question I can't handle with..


    In a modern car its fuel consumption is closely and continuously monitored by
    internal sensors. For a car traveling through a congested areas with heavy trac, the
    actual instantaneous fuel consumption
    X(t) is modeled by an Ornstein-Uhlenbeck

    process with lambda= 1[sec] second and sigma= 1[l=100 km] centered around a deterministic

    function m(t) that oscillates relatively slowly around 6 [l=100km] but has a shape

    that depends on the driving style of a particular driver.

    

    Recall properties of Ornstein-Uhlenbeck process de ned as a moving average
    process, such as a covariance function, continuity and di erentiability (or lack
    of it) properties, Markovian property.
    

    Suppose that a car manufacturer wants to show the instantaneous fuel con-
    sumption X(t) on the dashboard of a car. Discuss why it maybe not a good

    idea to do so. How showings of such a gauge would look like? Would it be very

    informative? Would it give an information to the driver that would allow him

    to adjust the shape of slowly changing m(t)?

    Thank you very much for any help



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