Differential and Integral Equations

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

T. E. Govindan

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Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060885

Mathematical Reviews number (MathSciNet)
MR1869824

Zentralblatt MATH identifier
1006.60053

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

Citation

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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