# Desmond J. Higham

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- Influence

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**public sources and our publisher partners.**A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler's method for deterministic differential… Expand

Proceedings of the National Academy of Sciences…

A fundamental issue in neuroscience is the relation between structure and function. However, gross landmarks do not correspond well to microstructural borders and cytoarchitecture cannot be… Expand

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state… Expand

Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients. In… Expand

Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain… Expand

BackgroundInterpretation of simple microarray experiments is usually based on the fold-change of gene expression between a reference and a "treated" sample where the treatment can be of many types… Expand

Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question "for what choices of stepsize does the numerical method reproduce the characteristics… Expand

The mean-reverting square root process is a stochastic differential equation (SDE) that has found considerable use as a model for volatility, interest rate, and other financial quantities. The… Expand

Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models… Expand

A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler's method for de- terministic differential… Expand