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Continuous dependence on coefficients for stochastic evolution equations with multiplicative lévy noise and monotone nonlinearity

Salavati, E ; Sharif University of Technology

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  1. Type of Document: Article
  2. Publisher: Iranian Mathematical Society
  3. Abstract:
  4. Semilinear stochastic evolution equations with multiplicative Lévy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of the continuity result, we derive sufficient conditions for asymptotic stability of the solutions, we show that Yosida approximations converge to the solution and we prove that solutions have Markov property. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed. The main tool in our study is an inequality which gives a pathwise bound for the norm of stochastic convolution integrals
  5. Keywords:
  6. Lévy processes ; Monotone nonlinearity ; Stochasic evolution equations ; Stochastic convolution integrals
  7. Source: Bulletin of the Iranian Mathematical Society ; Volume 42, Issue 1 , 2016 , Pages 175-194 ; 10186301 (ISSN)
  8. URL: http://bims.iranjournals.ir/article_751.html