Literature map
Regime-switching homogenization at the centre, surrounded by the averaging theory it rests on, the regime-switching models it expands, fast stochastic volatility, and switching in physics and biology.
The circle holds the works that expand a quantity around its fast-switching average, for a diffusion or an ordinary differential equation whose coefficients follow a fast Markov chain.
Hover over, tap or tab to a node for its summary and the relations it takes part in; click it or press Enter to open the work. Hover over an edge for its relation, or read the relations as a list below the map. Drag nodes to untangle. On a narrow screen the map scrolls sideways. The full citations are in the bibliography, and the timeline places the same works in time.
The relations as a list
- Cotton 2001 (thesis) – Cotton 2026: all orders: origin
- Yin & Zhang 1998 – Yin 2009: chain expansions
- Il'in et al. 1999 – Yin 2009: densities to option prices
- Khasminskii & Yin 1996 – Il'in et al. 1999: asymptotic series
- Yin & Zhang 1998 – Il'in et al. 1999: two-time-scale chains
- Basu & Ghosh 2009 – Yin 2009: fast and slow limits
- Huang et al. 2014 – Huang et al. 2016: weak limit
- Khas'minskii 1966 – Papanicolaou et al. 1977: averaging
- Khas'minskii 1966 – Khasminskii & Yin 1996: averaging
- Griego & Hersh 1969 – Kurtz 1973: random evolutions
- Kurtz 1973 – Papanicolaou et al. 1977: random evolutions
- Papanicolaou et al. 1977 – Bensoussan et al. 1978: probabilistic side
- Pavliotis & Stuart 2008 – Bensoussan et al. 1978: textbook
- Bensoussan et al. 1978 – Cotton 2026: all orders: corrector method
- Hamilton 1989 – Landén 2000: regime models
- Landén 2000 – Elliott & Siu 2009: semi-affine precursor
- Elliott & Siu 2009 – Elliott & Mamon 2002: generalizes
- van Beek et al. 2020 – Elliott & Siu 2009: affine on the enlarged state
- Rodrigo & Mamon 2021 – Elliott & Siu 2009: time-dependent coefficients
- Elliott & Mamon 2002 – Cotton 2001 (thesis): exact bond price, equal volatilities
- Vasicek 1977 – Cotton 2001 (thesis): the model in each regime
- Papanicolaou & Sircar 2014 – Yin 2009: slow regime shifts, the opposite limit
- Sircar & Papanicolaou 1999 – Fouque et al. 2000: fast volatility in option pricing
- Fouque et al. 2003 – Fouque et al. 2000: error analysis
- Fouque et al. 2000 – Cotton et al. 2004: fast-scale template
- Cotton et al. 2004 – Fouque et al. 2011: collected in
- DeSantiago et al. 2008 – Fouque et al. 2011: bond corrections
- Cotton et al. 2004 – Cotton 2026: all orders: chain replaces diffusion
- Anderson 1954 – Kubo 1954: the Kubo–Anderson model