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We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean field approximation.
We introduce a heterogeneous continuous time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environmen
Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L{e}vy walk, in which the particles are stocha
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a n
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation that relates