Related papers: Modelling Illiquid Stocks Using Quantum Stochastic…
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction…
The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the $\alpha$~-~quantile price is shown. The large Black-Scholes model is…
We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers' time. We also describe the connection between stochastic…
The reformulation of nonequilibirum thermodynamics, to include the treatment of thermodynamic fluctuations, is applied to the hydrodynamic fluctuations of a simple fluid. It is shown that the nonequilibrium thermodynamic scheme leads to the…
The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…
We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response…
We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and…
Presenting a general phase approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time dependent and stationary probability distributions. In one dimension we…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
The recent analysis on noncommutative geometry, showing quantization of the volume for the Riemannian manifold entering the geometry, can support a view of quantum mechanics as arising by a stochastic process on it. A class of stochastic…
The main concern of the present paper is the study of the multi-scale dynamics of thermonuclear fusion plasmas via a multi-species Fokker-Planck kinetic model. One of the goals is the generalization of the standard Fokker-Planck collision…
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation…
There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the…
In this work, we use scattering method to study the Kramers-Fokker-Planck equation with a potential whose gradient tends to zero at the infinity. For short-range potentials in dimension three, we show that complex eigenvalues do not…
We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson…
We show an equivalence between the approach of Buttiker and the Fermi quantum stochastic calculus for mesoscopic systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel…
We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…
We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting…