Jul 2026· WSEAS Transactions on Mathematics· Vol 25, pp. 269· 0 citations· 6 references
Abstract
The problem of minimizing the expected time spent by one-dimensional stochastic processes in a given interval is considered in the case of diffusion processes with random resettings. At random times that occur according to a Poisson process, the controlled diffusion process jumps from its current position to a fixed value. The differential equation satisfied by the value function is given and particular problems are solved explicitly.
In this paper, we study a piecewise-deterministic stochastic process governed by a double-well potential. The dynamics are randomised through resets to a random point, occurring after independent and exponentially distributed time intervals. Distributions of the particle’s position are presented for a fixed time, as we...
N. Ratanov· Markov Processes and Related...· 0 citations
We obtain a complete characterization of the quasi-stationary distributions of subcritical stable continuous-state branching processes in Brownian random environments, together with the domain of attraction of each member. These distributions form a one-parameter family whose modified Laplace transforms are given expli...
Using the local time-space calculus of Peskir (2005) and the method developed in Mijatovic (2010), we derive a new integral representation for the backward probability associated with the first-passage time (FPT) of a diffusion process through a time-dependent barrier. We present a complete three-step numerical algorit...
J. Detemple, Y. Kitapbayev, D. Shabalin· 1 citation
We study the law of the exit time and exit point of a Brownian motion in a two-dimensional domain with reflecting boundary conditions, except on small disjoint exit windows through which the stochastic process can escape the domain. In the limit of infinitely small exit windows, it is natural to assume that the process...
L. Carillo, T. Lelièvre, Thomas Normand et al.· 2 citations
A sequence of non-linear iterations with non-identically distributed random perturbations is studied. The asymptotic behaviour of the sequence is described via its visitations measures, which are deterministic measures that allow one to estimate the time spent by the sequence in the neighbourhoods of its partial limits...
A. Dorogovtsev, І. І. Ніщенко· Matematychni Studii· 0 citations
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