Differential and Integral Equations

An existence result for the Cauchy problem for stochastic systems with heredity

T. E. Govindan

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In this paper, we consider stochastic differential equations with heredity in a Hilbert space. In [14], the existence and uniqueness of a solution of such a class of systems was studied using linear growth and some less-restrictive conditions (Ousgood or Holder type) than the Lipschitz condition on the nonlinear terms. Our objective here is to study the existence problem by dropping even the linear growth condition and instead replacing it by some less restrictive conditions. We prove our existence result by the method of successive approximations and a comparison principle.

Article information

Differential Integral Equations, Volume 15, Number 1 (2002), 103-113.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K50: Stochastic functional-differential equations [See also , 60Hxx]
Secondary: 60H05: Stochastic integrals 60H10: Stochastic ordinary differential equations [See also 34F05]


Govindan, T. E. An existence result for the Cauchy problem for stochastic systems with heredity. Differential Integral Equations 15 (2002), no. 1, 103--113. https://projecteuclid.org/euclid.die/1356060885

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