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We develop a new split-step θ (SSθ) method for stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the SSθ method for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory

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Strong Convergence of the Split-Step<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:math>-Method for Stochastic Age-Dependent Capital System with Random Jump Magnitudes

Strong Convergence of the Split-Stepθ-Method for Stochastic Age-Dependent Capital System with Random Jump Magnitudes