23 citations · 27 across the 4 of their papers we have counts for
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Self-Similar Markov Processes on Cantor Set
Yuri Bakhtin
We define analogues of Brownian motion on the triadic Cantor set by introducing a few natural requirements on the Markov semigroup. We give a detailed description of these symmetri…
Poisson Limit for Associated Random Fields
Yuri Bakhtin
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of exampl…
Exit asymptotics for small diffusion about an unstable equilibrium
Yuri Bakhtin
A dynamical system perturbed by white noise in a neighborhood of an unstable fixed point is considered. We obtain the exit asymptotics in the limit of vanishing noise intensity. Th…
Existence And Uniqueness Of Stationary Solution Of Nonlinear Stochastic Differential Equation With Memory
Yuri Bakhtin
A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficie…