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On a class of parabolic differential equations driven with stochastic point processes

Published online by Cambridge University Press:  14 July 2016

K. Gopalsamy  and
A. T. Bharucha-Reid
K. Gopalsamy
Affiliation:
The Flinders University of South Australia
A. T. Bharucha-Reid
Affiliation:
Wayne State University, Detroit, Michigan
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Abstract

This paper is concerned with the solution of an initial and boundary value problem for a parabolic differential equation driven by a stochastic point process.

Keywords

RANDOM PARTIAL DIFFERENTIAL EQUATIONSTOCHASTIC POINT PROCESSGENERALIZED RANDOM FUNCTIONSPOISSON PROCESSCONFINEMENT PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 98 - 106
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Bharucha-Reid, A. T. (1960) Elements of the Theory of Markov Processes and Their Applications. McGraw-Hill, New York.Google Scholar
[2] Cox, D. R. and Miller, H. D. (1968) The Theory of Stochastic Processes. Wiley, New York.Google Scholar
[3] Dunford, N. and Schwartz, J. T. (1958) Linear Operators. Part I: General Theory. Wiley, New York.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and Its Applications. Vol. II. Wiley, New York.Google Scholar
[5] Mikhlin, S. G. (1965) The Problem of the Minimum of a Quadratic Functional. (Translated from the Russian), Holden-Day, San Francisco.Google Scholar
[6] Prohorov, Yu. V. and Rozanov, Yu. A. (1969) Probability Theory. (Translated from the Russian), Springer-Verlag, New York.Google Scholar
[7] Sobolev, S. L. (1964) Partial Differential Equations of Mathematical Physics. (Translated from the Russian), Pergamon Press, New York.Google Scholar
[8] Srinivasan, S. K. (1969) Stochastic Theory and Cascade Processes. American Elsevier, New York.Google Scholar
[9] Sz.-Nagy, B. (1953) Sur les contractions de l'éspace de Hilbert. Acta Sci. Math. Szeged 15, 87–92.Google Scholar
[10] Thomas, L. E. and Boyce, W. E. (1972) The behavior of a self-excited system acted upon by a sequence of random impulses. J. Differential Eqs. 12, 438–454.Google Scholar