Existence and uniqueness theorem for uncertain differential equations

  • Authors:

  • X. Chen;B. Liu

  • Affiliations:

  • Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing, China 100084;Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing, China 100084

  • Venue:
  • Fuzzy Optimization and Decision Making
  • Year:
  • 2010

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Abstract

Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear uncertain differential equations, and proves an existence and uniqueness theorem of solution for uncertain differential equation under Lipschitz condition and linear growth condition.