Randomly Perturbed Volterra Integral Equations And Some Applications

References

• Dorogovtsev , A.A. 1990 . Ito-Velterra equations with an anticipating right-handside in the absence of moments Infinite dimensional stochastic analysis . Akad Nauk Ukr. SSR, Inst. Math.Kiev , : 41 – 50 .
   Google Scholar
• Freidlin , M.J. and Wentzell , A.D. 1979 . “ Random perturbations of dynamical systems ” . NY : Springer-Verlag .
   Google Scholar
• Hoppensteadt , F.C. 1975 . “ Mathematical theories of populations: demographics, genetics and epidemics ” . Philadelphia, PA : CBMS, no.20, SLAM Publications .
   Google Scholar
• Hoppensteadt , F.C. 1982 . “ Mathematical methods of population biology ” . Cambridge, MA : Cambridge University Press .
   Google Scholar
• Hoppensteadt , F.C. , Khasminskii , R. and Salehi , H. 1994 . Asymptotic solutions of linear partial differential equations of first order having random coefficients . Random Oper. and Stoch. Equ , 2 : 77 – 93 .
   Google Scholar
• F.C. , Salehi , H. and Skorokhod , A. “ An averaging principle for dynamical systems in Hilbert space with Markov random perturbations ” . to appear
   Google Scholar
• Khasminskii , R. 1966 . On random processes determined by differential equations with small parameter . Teor. Veroyatnost. i Primen , 11 : 240 – 259 .
   Google Scholar
• Khasminskii , R.Z. 1968 . On the averaging principle for Ito stochastic differential equations . Kybernetica(prague) , 4 : 260 – 279 .
   Google Scholar
• Khasminskii , R.Z. 1968 . “ Stochastic stability of differential equations ” . In Sijinoff and Noordhoff Alphen aan den Rign Netherland
   Google Scholar
• Keyfitz , N. and Flieger , W. 1971 . “ Population, fact and methods of demography ” . SanFrancisco, CA : W. H. Freeman .
   Google Scholar
• Kushner , H.I. 1984 . “ Approximation and weak convergence methods for random processes with applications to stochastic system theory ” . Cambridge, MA : MIT Press .
   Google Scholar
• Lewin , M. 1987 . On the existence of a weak solution to an equation of Volterra-Skorokhod type . Libertas 'Math , 1 : 107 – 123 .
   Google Scholar
• Lewin , M. 1992 . Weak solutions to nonlinear Ito-Volterra equations in Hilbert spaces . Stochastic Analysis and Applications , 10 : 443 – 464 .
   Web of Science ®Google Scholar
• Lindsey , W. C. 1972 . “ Synchronization systems in communication and control ” . EnglewoodCliffs, NJ : Prentice-Hall .
   Google Scholar
• Murge , M.G. and Pachpatte , B.G. 1988 . On a generalized to type Stochastic hereditary equation . Demonstratio Math , 21 : 77 – 103 .
   Google Scholar
• Papanicolaou , G. C. 1988 . Asymptotic analysis of transport processes . BAMS , 81 : 330 – 392 .
   Google Scholar
• Papanicolaou , G.C. , Stroock , D.W. and Varadhan , S.R.S. 1977 . “ Martingale approach to some limit theorems ” . Vol. 3 , Durham, NC : Duke Univ. Math. Ser .
   Google Scholar
• Pardoux , E. and Protter , P. 1990 . Stochastic Volterra equations with anticipating coefficients . Ann. Prob , 18 : 1635 – 1655 .
   Web of Science ®Google Scholar
• Pikovskii , I.E. 1990 . Existence and uniqueness of a strong solution of a stochastic integral equation of Ito-Volterra type . Theory Probab. Math. Statist , 41 : 115 – 120 .
   Google Scholar
• Prohorov , Yu.V. and Rozanov , Yu.A. 1969 . “ Probability theory, Basic concept ” . In Limit theorems, Random processes , NY : Springer-Verlag .
   Google Scholar
• Shevlyakov , A.Y. 1988 . On stochastic integral equations . Theory Probab. Math. Statist , 38 : 127 – 135 .
   Google Scholar
• Skorokhod , A.V. 1989 . “ Asymptotic methods in the theory of stochastic differential equations ” . In Trans. Math. Monographs 78 AMS Providence, RI
   Google Scholar