Numerical methods for a class of jump–diffusion systems with random magnitudes

Stochasticθ-Methods for a Class of Jump-Diffusion Stochastic Pantograph Equations with Random Magnitude

“…The analysis uses ideas from [ 15 ], where analogous results are derived in the stochastic differential equations. By construction, we have Now for any 0 ≤ t 1 ≤ T we have By Assumption 1 and Hölder inequality, we have …”

“…In [ 9 – 13 ] strong convergence and mean-square stability properties were analysed in the case of Poisson-driven jumps of deterministic magnitude. References [ 14 , 15 ] discussed the numerical methods of stochastic differential equations with random jump magnitudes. Motivated by the papers above, in this paper, we focus on stochastic pantograph equations with random jump magnitudes.…”

A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes

“…Stochastic differential equations with compound Poisson processes have been commonly used in mathematical finance and covering a wide range of finance models [13][14][15][16]. Considering the aftereffect of the past state, Jiang et al [17] proposed a semiimplicit Euler numerical method for stochastic differential delay equations with Poisson driven jumps of random magnitudes. Furthermore, Mao [18] studied the stochastic differential equations with variable delays and random jump magnitudes (SDEVDRJMs) which are of the form…”