12 citations · 39 across the 16 of their papers we have counts for
17 papers
Extreme ATM skew in a local volatility model with discontinuity: joint density approach
Alexander Gairat, Vadim Shcherbakov
This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given…
Balls-in-bins models with asymmetric feedback and reflection
Mikhail Menshikov, Vadim Shcherbakov
Balls-in-bins models describe a random sequential allocation of infinitely many balls into a finite number of bins. In these models a ball is placed into a bin with probability pro…
Skew Brownian motion with dry friction: joint density approach
Alexander Gairat, Vadim Shcherbakov
This note concerns distributions of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in [2] by using the Laplace transform and join…
Discrete SIR model on a homogeneous tree and its continuous limit
Alexander Gairat, Vadim Shcherbakov
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the t…
Linear competition processes and generalized Polya urns with removals
Serguei Popov, Vadim Shcherbakov, Stanislav Volkov
A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a co…
Localisation in a growth model with interaction. Arbitrary graphs
Mikhail Menshikov, Vadim Shcherbakov
This paper concerns the long term behaviour of a growth model describing a random sequential deposition of particles on a finite graph. The probability of allocating a particle at…
Long term behaviour of a reversible system of interacting random walks
Svante Janson, Vadim Shcherbakov, Stanislav Volkov
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of…
Boundary effect in competition processes
Vadim Shcherbakov, Stanislav Volkov
This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction.…
Localisation in a growth model with interaction
Marcelo Costa, Mikhail Menshikov, Vadim Shcherbakov +1
This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinfor…
A note on scaling limits for truncated birth-and-death processes with interaction
Vadim Shcherbakov, Anatoly Yambartsev
In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov c…
Long term behaviour of two interacting birth-and-death processes
Mikhail Menshikov, Vadim Shcherbakov
In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is model…
Density of Skew Brownian motion and its functionals with application in finance
Alexander Gairat, Vadim Shcherbakov
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volat…
Long term behaviour of locally interacting birth-and-death processes
Vadim Shcherbakov, Stanislav Volkov
In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed descript…
Asymptotic normality of maximum likelihood estimator for cooperative sequential adsorption
Mathew D. Penrose, Vadim Shcherbakov
We have shown in previous work that statistical inference for cooperative sequential adsorption model can be based on maximum likelihood estimation. In this paper we continue this…
Queueing with neighbours
Vadim Shcherbakov, Stanislav Volkov
In this paper we study asymptotic behaviour of a growth process generated by a semi-deterministic variant of cooperative sequential adsorption model (CSA). This model can also be v…
Stability of a growth process generated by monomer filling with nearest-neighbour cooperative effects
Vadim Shcherbakov, Stanislav Volkov
We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed pa…
Asymptotic analysis of a particle system with mean-field interaction
A. Manita, V. Shcherbakov
We study a system of interacting particles on . The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair…