19 citations · 99 across the 20 of their papers we have counts for
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The persistence exponents of Gaussian random fields connected by the Lamperti transform
George Molchan
The (fractional) Brownian sheet is a simplest example of a Gaussian random field X whose covariance is the tensor product of a finite number (d) of nonnegative correlation function…
Leadership exponent in the pursuit problem for 1-D random particles
G. Molchan
For n + 1 particles moving independently on a straight line, we study the question of how long the leading position of one of them can last. Our focus is the asymptotics of the pro…
Factional Brownian motion with multivariate time in a large convex area: persistence exponents
G. Molchan
The fractional Brownian motion of index , H-FBM, with d-dimensional time is considered on an expanding set TG, where G is a bounded convex domain that contains 0 at its…
Survival exponents for some Gaussian processes
George Molchan
The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated…
On the uniqueness of the branching parameter for a random cascade measure
G. Molchan
An independent random cascade measure is specified by a random generator, a vector of dimension c with non-negative components. The dimension c is called the branching cascade para…