Related papers: Feynman-Kac Equations for Reaction and Diffusion P…
The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport…
In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional L\'{e}vy process with moments of all orders. The results are important from a…
Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
We present a generalized integral fluctuation theorem (GIFT) for general diffusion processes using the Feynman-Kac and Cameron-Martin-Girsanov formulas. Existing IFTs can be thought of to be its specific cases. We interpret the origin of…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization.
We study stability of stationary solutions for a class of non-local semilinear parabolic equations. To this end, we prove the Feynman--Kac formula for a L\'{e}vy processes with time-dependent potentials and arbitrary initial condition. We…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
We present a study exploring the range of applicability of a generalized Fick Jacobs equation in the case when diffusive mass transport of a fluid along a pore includes chemical reactions in the bulk and pore surface. The study contemplates…
We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as…
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
The reaction of volatile matter plays an important role in the process of bringing matter from the surface of the planet to the atmosphere. Therefore, by simulating the mixing and chemical reaction process of volatile matter in the…
We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…