Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes | Zendy

Graeme D. Chalmers | Zendy; Desmond J. Higham | Zendy

Open Access

Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes

Author(s) -

Graeme D. Chalmers,

Desmond J. Higham

Publication year - 2008

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2008.9.47

Subject(s) - convergence (economics) , mathematics , stability (learning theory) , stochastic differential equation , jump , poisson distribution , jump process , computer science , statistics , physics , economics , quantum mechanics , machine learning , economic growth

Stochastic differential equations with Poisson driven jumps of random magnitude are popular as models in mathematical finance. Strong, or pathwise, simulation of these models is required in various settings and long time stability is desirable to control error growth. Here, we examine strong convergence and mean-square stability of a class of implicit numerical methods, proving both positive and negative results. The analysis is backed up with numerical experiments.

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