We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
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.
Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
Article purchase
Temporarily unavailable
References
[1]
[1]Bharucha-Reid, A. T. (1960) Elements of the Theory of Markov Processes and Their Applications.McGraw-Hill, New York.Google Scholar
[2]
[2]Cox, D. R. and Miller, H. D. (1968) The Theory of Stochastic Processes.Wiley, New York.Google Scholar
[3]
[3]Dunford, N. and Schwartz, J. T. (1958) Linear Operators. Part I: General Theory.Wiley, New York.Google Scholar
[4]
[4]Feller, W. (1966) An Introduction to Probability Theory and Its Applications.Vol. II. Wiley, New York.Google Scholar
[5]
[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]
[6]Prohorov, Yu. V. and Rozanov, Yu. A. (1969) Probability Theory.(Translated from the Russian), Springer-Verlag, New York.Google Scholar
[7]
[7]Sobolev, S. L. (1964) Partial Differential Equations of Mathematical Physics.(Translated from the Russian), Pergamon Press, New York.Google Scholar
[8]
[8]Srinivasan, S. K. (1969) Stochastic Theory and Cascade Processes.American Elsevier, New York.Google Scholar
[9]
[9]Sz.-Nagy, B. (1953) Sur les contractions de l'éspace de Hilbert. Acta Sci. Math. Szeged15, 87–92.Google Scholar
[10]
[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