On the behavior of the fundamental solution of the heat equation with variable coefficients

By S. Varadhan. 2010

310 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/63d0b4eebaafa2a6f8cae00d94186f3781132bfb

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In Computational Theory and Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL (2009, background): “All these articles are essentially higher order corrections and/or applications of the seminal work of Varadhan [23, 24], who showed that the small-time behavior of a diffusion process can be characterized in”
Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “In a similar spirit, cf. [54, Sec 5, Rmk 2.9], the Varadhan-type formula 2t log f (y, t) ∼ −d2 (x0, y), when l d, could be shown, without any conditions on (x0, y) by large deviation methods, only relying on the existence of a reasonable density.”
Geodesics in heat: A new approach to computing distance based on heat flow (2012, background): “where d(x, γ) is the shortest geodesic distance from x to γ [Varadhan 1967].”
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model (2009, unknown): “In this paper, we leverage on the heat kernel methods introduced for the study of stochastic processes by Varadhan [Var67a, Var67b] and used for the SABR model in [HLW05] and [HL05].”
The local entropy along Ricci flow---Part A: the no-local-collapsing theorems (2017, background): “which is a large deviation formula dates back to Varadhan [50].”
Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, methodology): “In that case we have Q = n and formula (2) is the celebrated Varadhan formula obtained in [56].”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, unknown): “, [118], [119], [37].”
Probability Distribution in the SABR Model of Stochastic Volatility (2015, methodology): “To extract usable asymptotic information about the transition probability, more accurate analysis is necessary, but the choice of the Riemannian structure on U dictated by Varadhan’s theorem turns out to be key.”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, background): “A famous result due to Varadhan [167], in the setting of diffusions on Euclidean space with elliptic generator, states that the lim sup above can be replace by a genuine limit and equality holds.”