Mean-square stability of a class of stochastic integral equations
نویسندگان
چکیده
منابع مشابه
A-stability and Stochastic Mean-square Stability∗
This note extends and interprets a result of Saito and Mitsui [SIAM J. Numer. Anal., 33 (1996), pp. 2254–2267] for a method of Milstein. The result concerns mean-square stability on a stochastic differential equation test problem with multiplicative noise. The numerical method reduces to the Theta Method on deterministic problems. Saito and Mitsui showed that the deterministic A-stability prope...
متن کاملMean-Field Backward Stochastic Volterra Integral Equations
Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...
متن کاملExponential Stability in Mean Square for a General Class of Discrete-time Linear Stochastic Systems
The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability...
متن کاملExponential Mean-square Stability of Numerical Solutions to Stochastic Differential Equations
Positive results are proved here about the ability of numerical simulations to reproduce the exponentialmean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step si...
متن کاملPreserving exponential mean-square stability in the simulation of hybrid stochastic differential equations
Positive results are derived concerning the long time dynamics of fixed stepsize numerical simulations of stochastic differential equation systems with Markovian switching. Euler–Maruyama and implicit theta-method discretizations are shown to capture exponential mean-square stability for all sufficiently small timesteps under appropriate conditions. Moreover, the decay rate, as measured by the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1972
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700045184