Related papers: Modeling solutions with jumps for rate-independent…
A recent line of work has shown remarkable behaviors of the generalization error curves in simple learning models. Even the least-squares regression has shown atypical features such as the model-wise double descent, and further works have…
We establish an integration by parts formula based on jumps times in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps.
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest…
In this study, we consider the exponential utility maximization problem in the context of a jump-diffusion model. To solve the problem, we rely on the dynamic programming principle and we derive from it a quadratic BSDE with jumps. Since…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…
The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter model ``dust'' fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue that…
We consider a one-dimensional kinetic model of granular media in the case where the interaction potential is quadratic. Taking advan- tage of a simple first integral, we can use a reformulation (equivalent to the initial kinetic model for…
On the basis of the viscous Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. Thanks to the inclusion of viscosity, the jumps are not abrupt, rendering the classic patchwork…
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in…
We consider a toy model of rate independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We introduce a notion of solutions based on an obstacle problem. These solutions…
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 propose a novel class of flexible latent-state time series regression models which we call Markov-switching generalized additive models for location, scale and shape. In contrast to conventional Markov-switching regression models, the…
We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying…
We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with…