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On the solution of Kac-type partial differential equations

Part of: Stochastic analysis Inference from stochastic processes Parabolic equations and systems

Published online by Cambridge University Press:  14 July 2016

Mátyás Arató
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Abstract

The Cauchy problem in the form of (1.11) with linear and constant coefficients is discussed. The solution (1.10) can be given in explicit form when the stochastic process is a multidimensional autoregression (AR) type, or Ornstein–Uhlenbeck process. Functionals of (1.10) form were studied by Kac in the Brownian motion case. The solutions are obtained with the help of the Radon–Nikodym transformation, proposed by Novikov [12].

Keywords

AUTOREGRESSIONCAUCHY PROBLEMBROWNIAN MOTIONRADON–NIKODYM DERIVATIVESTOCHASTIC FUNCTIONALSDISTRIBUTIONSLAPLACE TRANSFORMPARTIAL DIFFERENTIAL EQUATIONS

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 62M10: Time series, auto-correlation, regression, etc. 35K99: None of the above, but in this section

Information

Type
Part 6 Stochastic Processes
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 311 - 324
Copyright
Copyright © Applied Probability Trust 1994 

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References

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