Numerical solutions of neutral stochastic functional differential equations with Markovian switching
نویسندگان
چکیده
منابع مشابه
Stochastic Functional Differential Equations with Markovian Switching
The main aim of this paper is to investigate the exponential stability of stochastic functional differential equations with Markovian switching. The Razumikhin argument and the generalized Itô formula will play their important roles in this paper. Applying our new results to several important types of equations e.g. stochastic differential delay equations and stochastic differential equations, ...
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and Applied Analysis 3 + 4Lλ 2 j μ g (0, j) 2 HS + λj g (0, j) 2 HS ≤ − μ 2 ‖x‖ 2 H + α 1 , ∀x ∈ H, j ∈ S, (9) whereα 1 := max j∈S[(4λ 2 j ‖ f(0, j)‖ 2 H /μ) +(4Lλ 2 j /μ) ‖ g(0, j) ‖ 2 HS + λj ‖ g(0, j)‖ 2 HS] and ⟨T, S⟩HS := ∑ ∞ i=1 ⟨Te i , Se j ⟩ H for S, T ∈ LHS(H). Denote byZ(t) = (Xx,i(t), ri(t)) themild solution of (4) starting from (x, i) ∈ H × S. For any subset A ∈ B(...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2019
ISSN: 1687-1847
DOI: 10.1186/s13662-019-1957-z