Related papers: Conditional probabilities in multiplicative noise …
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
By departing from the previous attempt (Phys. Rev. {\bf E 51}, 4114, (1995)) we give a detailed construction of conditional and perturbed Markov processes, under the assumption that the Cauchy law of probability replaces the Gaussian law…
The ability to quantify stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression…
We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and genes dynamics, with…
In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible…
In this paper, we established a quadratic transportation cost inequality for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise based on a new inequality we proved for the moments (under the…
We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
In this paper, we study a class of dissipative stochastic differential equations driven by nonlinear multiplicative fractional Brownian noise with Hurst index $H \in \left(\frac{1}{3},\frac{1}{2})\cup(\frac{1}{2}, 1\right) $. We establish…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…