Related papers: Polynomial jump-diffusions on the unit simplex
In this paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
Consider jump-type stochastic differential equations with the drift, diffusion and jump terms. Logarithmic derivatives of densities for the solution process are studied, and the Bismut-Elworthy-Li type formulae can be obtained under the…
We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition…
We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear…
We extend some known results relating the distribution tails of a continuous local martingale supremum and its quadratic variation to the case of locally square integrable martingales with bounded jumps. The predictable and optional…
The misanthrope process is a class of stochastic interacting particle systems, generalizing the simple exclusion process. It allows each site of the lattice to accommodate more than one particle. We consider a special case of the one…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The…
In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and…
We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\R^d$ with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency…
We consider quasi-polynomial spaces of differential forms defined as weighted (with a positive weight) spaces of differential forms with polynomial coefficients. We show that the unisolvent set of functionals for such spaces on a simplex in…
A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The extinction and explosion probabilities and the mean extinction and…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…