We present a method for constructing new families of solvable one-dimensional diffusions with linear drift and nonlinear diffusion coefficient functions, whose transition densities are obtainable in analytically closed-form. Our approach is based on the so-called diffusion canonical transformation method that allows us to uncover new multiparameter diffusions that are mapped onto various simple...

This paper develops an eigenfunction expansion approach to solve discretely monitored first passage time problems for a rich class of Markov processes, including diffusions and subordinate diffusions with jumps, whose transition or Feynman-Kac semigroups possess eigenfunction expansions in L spaces. Many processes important in finance are in this class, including OU, CIR, (JD)CEV diffusions and...

We dedicate this paper to Sir John Kingman on his 70th Birthday. In modern mathematical population genetics the ancestral history of a population of genes back in time is described by John Kingman’s coalescent tree. Classical and modern approaches model gene frequencies by diffusion processes. This paper, which is partly a review, discusses how coalescent processes are dual to diffusion process...

Parameters of Gasser Leutwyler chiral Lagrangian are proved saturated by dynamical quark self energy Σ(k2) in a gauge invariant, nonlocal, dynamical quark model. Much of low-energy QCD can be encoded into a series parameters appearing in a chiral Lagrangian, expanded to some finite order of low energy expansion. Attempts have been made to understand these parameters: it is shown that low lying ...

Emissions of CO2 and CH4 from freshwater reservoirs constitute a globally significant source of atmospheric greenhouse gases (GHGs), but knowledge gaps remain with regard to spatiotemporal drivers of emissions. We document the spatial and seasonal variation in surface diffusion of CO2 and CH4 from Douglas Lake, a hydropower reservoir in Tennessee, USA. Monthly estimates across 13 reservoir site...

With the help of the methods developed in [21], we highlight condition (T ) as a source of new examples of ’ballistic’ diffusions in a random environment when d ≥ 2 (’ballistic’ means that a strong law of large numbers with non-vanishing limiting velocity holds). In particular we are able to treat the case of non-constant diffusion coefficients, a feature that causes problems. Further we recove...

This paper considers pricing European options in a large class of one-dimensional Markovian jump processes known as subordinate diffusions, which are obtained by time changing a diffusion process with an independent Lévy or additive random clock. These jump processes are nonLévy in general, and they can be viewed as natural generalization of many popular Lévy processes used in finance. Subordin...

This paper provides explicit analytical characterizations for first hitting time densities for Cox–Ingersoll–Ross (CIR) and Ornstein–Uhlenbeck (OU) diffusions in terms of relevant Sturm–Liouville eigenfunction expansions. Starting with Vasicek (1977) and Cox, Ingersoll and Ross (1985), the Gaussian Ornstein– Uhlenbeck and Feller’s (1951) square-root diffusions are among the most commonly used s...

In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jacobi equations (erosions) on the space R o S of 3D-positions and orientations naturally embedded in the group SE(3) of 3Drigid body movements. The general motivation for these (convection-)diffusions and erosions is to obtain crossingpreserving fiber enhancement on probability densities defined on...

In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to −∞ at the origin, and the diffusion to have an entrance boundary at +∞. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth–death processes. Generalized Fe...