We review recent applications of jump models for diffusion in zeolites. We describe the results of a coarse-grained model of the interplay between zeolite anisotropy and disorder, finding that certain disorder patterns can change how anisotropy controls membrane permeation. We show the results of a lattice model for single-file diffusion in zeolite membranes, demonstrating how single-file motio...

This paper presents everything you need to know about Merton jump diffusion (we call it MJD) model. MJD model is one of the first beyond Black-Scholes model in the sense that it tries to capture the negative skewness and excess kurtosis of the log stock price density ( ) 0 ln( / ) T S S P by a simple addition of a compound Possion jump process. Introduction of this jump process adds three extra...

Deep neural networks (DNNs) with ReLU activation function are proved to be able express viscosity solutions of linear partial integrodifferential equations (PIDEs) on state spaces possibly high dimension d. Admissible PIDEs comprise Kolmogorov for high-dimensional diffusion, advection, and pure jump Lévy processes. We prove such arising from a class jump-diffusions [Formula: see text], that any...

We construct a sequence of functions that uniformly converge (on compact sets) to the price of an Asian option, which is written on a stock whose dynamics follow a jump diffusion. The convergence is exponentially fast. We show that each element in this sequence is the unique classical solution of a parabolic partial differential equation (not an integro-differential equation). As a result we ob...

Opinions, and subsequently opinion dynamics, depend not just on interactions among individuals, but also on external influences such as the mass media. The dependence on local interactions, however, has received considerably more attention. In this paper, we use the classical voter model as a basis, and extend it to include external influences. We show that this new model can be understood usin...

1. Introduction Carbon interstitial diffusion in austenite (γ-Fe) has been studied experimentally and analytically for many years. Two experimental studies have been made of carbon diffusion in austenite at low carbon contents. One is a measurement of the carbon chemical or intrinsic diffusion coefficient at 1075 K, 1124 K and 1273 K, and as a function of carbon content [1]; the other is a meas...

In this paper we consider the optimal trading strategy for an investor with an exponentially distributed horizon who invests in a riskless asset and a risky asset. The risky asset is subject to proportional transaction costs and its price follows a jump diffusion. In this situation, the optimal trading strategy is to maintain the fraction of the dollar amount invested in the riskless asset to t...

Abstract We investigate scaling limits of the seed bank model when migration (to and from bank) is ‘slow’ compared to reproduction. This motivated by models for bacterial dormancy, where periods dormancy can be orders magnitude larger than reproductive times. Speeding up time, we encounter a separation timescales phenomenon which leads mathematically interesting observations, in particular prov...

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 finite collection of time points. Within this framework we extend existing exact algorithms and introduce novel adaptive approaches. We consider an application...