Fundamental solutions to Kolmogorov equations via reduction to canonical form

This paper finds fundamental solutions to the backward Kolmogorov equations, usually interpretable as transition density functions for variables x that follow certain stochastic processes of the form dx=A(x,t)dt

[1]  W. Feller TWO SINGULAR DIFFUSION PROBLEMS , 1951 .

[2]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[3]  HO THOMASS.Y.,et al.  Term Structure Movements and Pricing Interest Rate Contingent Claims , 2007 .

[4]  A. Kuznetsov,et al.  Transformations of Markov Processes and Classification Scheme for Solvable Driftless Diffusions , 2007, 0710.1596.

[5]  G. Bluman,et al.  ON THE TRANSFORMATION OF DIFFUSION PROCESSES INTO THE WIENER PROCESS , 1980 .

[6]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[7]  William Feller,et al.  Diffusion Processes in Genetics , 1951 .

[8]  A. Aksenov,et al.  CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 2. Applications in Engineering and Physical Sciences , 1995 .

[9]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[10]  Eckhard Platen,et al.  Symmetry group methods for fundamental solutions , 2004 .

[11]  P. Wilmott Derivatives: The Theory and Practice of Financial Engineering , 1998 .

[12]  S. Beckers The Constant Elasticity of Variance Model and Its Implications For Option Pricing , 1980 .

[13]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[14]  Campbell R. Harvey,et al.  An Empirical Comparison of Alternative Models of the Short-Term Interest Rate , 1992 .

[15]  Comparison of the performance of a time‐dependent short‐interest rate model with time‐independent models , 2004 .

[16]  Jianqing Fan,et al.  Time-dependent Diffusion Models for Term Structure Dynamics and the Stock Price Volatility , 2003 .

[17]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .