Related papers: Convergence of hitting times for jump-diffusion pr…

For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here we show convergence of the so-called finite system scheme for interacting…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If $X(t)$ is a one-dimensional diffusion with jumps, starting from…

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a…

Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a…

In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for…

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…

We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data

We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by…

In this paper, we establish smoothness of moments of the solutions of discrete coagulation-diffusion systems. As key assumptions, we suppose that the coagulation coefficients grow at most sub-linearly and that the diffusion coefficients…

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…

This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the…

One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The…

For a class of time-inhomogeneous SDEs with jumps, we establish criteria for the existence and uniqueness of the nonnegative solutions, and examine the extinction, the explosion together with the contractivity of the solutions, which…

This work develops Feynman-Kac formulas for a class of regime-switching jump diffusion processes, in which the jump part is driven by a Poisson random measure associated to a general L\'evy process and the switching part depends on the jump…

The paper is focused on the numerical solution of stochastic reaction-diffusion problems. A special attention is addressed to the conservation of mean-square dissipativity in the time integration of the spatially discretized problem,…

We study the dispersion of a particle whose motion dynamics can be described by a forced velocity jump process. To investigate large deviations results, we study the Chapman-Kolmogorov equation of this process in the hyperbolic scaling…

We investigate the utility in employing asymptotic results related to a clustering criterion to the problem of testing for the presence of jumps in financial models. We consider the Jump Diffusion model for option pricing and demonstrate…

Autoregressive processes are intensively studied in statistics and other fields of applied stochastics. For many applications the overshoot and the threshold-time are of special interest. When the upward innovations are in the class of…

We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is…