The Numerical Invariant Measure of Stochastic 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, ...
متن کاملStochastic Differential Equations with Multi-Markovian Switching
Owing to their theoretical and practical significance, (1) has received great attention and has been recently studied extensively, andwe heremention Skorokhod [1] andMao and Yuan [2] among many others. However, in the real world, the condition that coefficients f and g in (1) are perturbed by the same Markovian chain is too restrictive. For example, in the classical Black-Scholes model, the ass...
متن کاملNeutral Stochastic Differential Delay Equations with Markovian Switching
Neutral stochastic differential delay equations (NSDDEs) have recently been studied intensively (see Kolmanovskii, V.B. and Nosov, V.R., Stability and Periodic Modes of Control Systems with Aftereffect; Nauka: Moscow, 1981 and Mao X., Stochastic Differential Equations and Their Applications; Horwood Pub.: Chichester, 1997). Given that many systems are often subject to component failures or repa...
متن کاملStationary in Distributions of Numerical Solutions for Stochastic Partial Differential Equations with Markovian Switching
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(...
متن کاملApproximations of Numerical Method for Neutral Stochastic Functional Differential Equations with Markovian Switching
Stochastic systems with Markovian switching have been used in a variety of application areas, including biology, epidemiology, mechanics, economics, and finance. In this paper, we study the Euler-Maruyama EM method for neutral stochastic functional differential equations with Markovian switching. The main aim is to show that the numerical solutions will converge to the true solutions. Moreover,...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2018
ISSN: 0036-1429,1095-7170
DOI: 10.1137/17m1143927