Stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity

Document Type: Research Paper

Authors

1 School of Mathematics‎, ‎Institute for Research in Fundamental Sciences (IPM)‎, ‎P.O‎. ‎Box 19395-5746‎, ‎Tehran‎, ‎Iran ‎ ‎Faculty of Mathematics and Computer Science‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran.

2 Department of Mathematics‎, ‎Sharif University of Technology‎, ‎Tehran‎, ‎Iran.

Abstract

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed‎.

Keywords

Main Subjects


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Volume 43, Issue 5
September and October 2017
Pages 1287-1299
  • Receive Date: 10 October 2015
  • Revise Date: 18 May 2016
  • Accept Date: 23 May 2016