Related papers: Density Approximation of Affine Jump Diffusions vi…
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess…
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
We introduce ajdmom, a Python package designed for automatically deriving moment formulae for the well-established affine jump diffusion processes with state-independent jump intensities. ajdmom can produce explicit closed-form expressions…
Guided diffusion sampling relies on approximating often intractable likelihood scores, which introduces significant noise into the sampling dynamics. We propose using adaptive moment estimation to stabilize these noisy likelihood scores…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for affine jump-diffusions with a canonical state…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
An integro-differential equation for the probability density of the generalized stochastic Ornstein-Uhlenbeck process with jump diffusion is considered. It is shown that for a certain ratio between the intensity of jumps and the speed of…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
A jump-diffusion process along with a particle scheme is devised as an accurate and efficient particle solution to the Boltzmann equation. The proposed process (hereafter Gamma-Boltzmann model) is devised to match the evolution of all…
To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…